共查询到20条相似文献,搜索用时 31 毫秒
1.
L. Adiels G. Backenstoss I. Bergström S. Carius S. Charalambous M. D. Cooper Ch. Findeisen D. Hatzifotiadou M. Hugi A. Kerek H. O. Meyer P. Pavlopoulos J. Repond L. Tauscher D. Tröster M. C. S. Williams K. Zioutas 《Zeitschrift fur Physik C Particles and Fields》1987,35(1):15-19
The branching ratios of \(p\bar p\) annihilations into the neutral final states 2π0, π0γ, and 2γ are measured by stopping antiprotons in liquid hydrogen. They are \(B_{2\pi ^0 } = \left( {2.06 \pm 0.14} \right) \times 10^{ - 4} \) , \(B_{\pi ^0 \gamma } = \left( {1.74 \pm 0.22} \right) \times 10^{ - 5} \) , andB γγ<1.7×10?6 (95% c.l.). 相似文献
2.
We consider the time-dependent Schrödinger-Hartree equation (1) $$iu_t + \Delta u = \left( {\frac{1}{r}*|u|^2 } \right)u + \lambda \frac{u}{r},(t, x) \in \mathbb{R} \times \mathbb{R}^3 ,$$ (2) $$u(0,x) = \phi (x) \in \Sigma ^{2,2} ,x \in \mathbb{R}^3 ,$$ where λ≧0 and \(\Sigma ^{2,2} = \{ g \in L^2 ;\parallel g\parallel _{\Sigma ^{2,2} }^2 = \sum\limits_{|a| \leqq 2} {\parallel D^a g\parallel _2^2 + \sum\limits_{|\beta | \leqq 2} {\parallel x^\beta g\parallel _2^2< \infty } } \} \) . We show that there exists a unique global solutionu of (1) and (2) such that $$u \in C(\mathbb{R};H^{1,2} ) \cap L^\infty (\mathbb{R};H^{2,2} ) \cap L_{loc}^\infty (\mathbb{R};\Sigma ^{2,2} )$$ with $$u \in L^\infty (\mathbb{R};L^2 ).$$ Furthermore, we show thatu has the following estimates: $$\parallel u(t)\parallel _{2,2} \leqq C,a.c. t \in \mathbb{R},$$ and $$\parallel u(t)\parallel _\infty \leqq C(1 + |t|)^{ - 1/2} ,a.e. t \in \mathbb{R}.$$ 相似文献
3.
We study subadditive functions of the random parking model previously analyzed by the second author. In particular, we consider local functions S of subsets of ${\mathbb{R}^d}$ and of point sets that are (almost) subadditive in their first variable. Denoting by ξ the random parking measure in ${\mathbb{R}^d}$ , and by ξ R the random parking measure in the cube Q R = (?R, R) d , we show, under some natural assumptions on S, that there exists a constant ${\overline{S} \in \mathbb{R}}$ such that $$\lim_{R \to +\infty} \frac{S(Q_R, \xi)}{|Q_R|} \, = \, \lim_{R \to +\infty} \frac{S(Q_R, \xi^{R})}{|Q_R|} \, = \, \overline{S}$$ almost surely. If ${\zeta \mapsto S(Q_R, \zeta)}$ is the counting measure of ${\zeta}$ in Q R , then we retrieve the result by the second author on the existence of the jamming limit. The present work generalizes this result to a wide class of (almost) subadditive functions. In particular, classical Euclidean optimization problems as well as the discrete model for rubber previously studied by Alicandro, Cicalese, and the first author enter this class of functions. In the case of rubber elasticity, this yields an approximation result for the continuous energy density associated with the discrete model at the thermodynamic limit, as well as a generalization to stochastic networks generated on bounded sets. 相似文献
4.
A. Lenard 《Communications in Mathematical Physics》1973,30(1):35-44
A general criterion is derived which assures the uniqueness of the state of a classical statistical mechanical system in terms of a given system of correlation functions. The criterion is \(\sum\limits_k {(m_{k + j}^A )} ^{ - 1/k} = \infty\) for allj and all bounded setsA, where $$m_k^A = (k!)^{ - 1} \int\limits_A \cdots \int\limits_A {\varrho _k } (x_1 , \ldots ,x_k )dx_1 \ldots dx_1 .$$ 相似文献
5.
Dongho Chae 《Communications in Mathematical Physics》2014,326(1):37-48
In this paper we study the Liouville-type properties for solutions to the steady incompressible Euler equations with forces in ${\mathbb {R}^N}$ . If we assume “single signedness condition” on the force, then we can show that a ${C^1 (\mathbb {R}^N)}$ solution (v, p) with ${|v|^2+ |p| \in L^{\frac{q}{2}}(\mathbb {R}^N),\,q \in (\frac{3N}{N-1}, \infty)}$ is trivial, v = 0. For the solution of the steady Navier–Stokes equations, satisfying ${v(x) \to 0}$ as ${|x| \to \infty}$ , the condition ${\int_{\mathbb {R}^3} |\Delta v|^{\frac{6}{5}} dx < \infty}$ , which is stronger than the important D-condition, ${\int_{\mathbb {R}^3} |\nabla v|^2 dx < \infty}$ , but both having the same scaling property, implies that v = 0. In the appendix we reprove Theorem 1.1 (Chae, Commun Math Phys 273:203–215, 2007), using the self-similar Euler equations directly. 相似文献
6.
Claudio Mu?oz 《Communications in Mathematical Physics》2012,314(3):817-852
In this paper we study soliton-like solutions of the variable coefficients, the subcritical gKdV equation $$u_t + (u_{xx} -\lambda u + a(\varepsilon x) u^m )_x =0,\quad {\rm in} \quad \mathbb{R}_t\times\mathbb{R}_x, \quad m=2,3\,\, { \rm and }\,\, 4,$$ with ${\lambda\geq 0, a(\cdot ) \in (1,2)}$ a strictly increasing, positive and asymptotically flat potential, and ${\varepsilon}$ small enough. In previous works (Mu?oz in Anal PDE 4:573?C638, 2011; On the soliton dynamics under slowly varying medium for generalized KdV equations: refraction vs. reflection, SIAM J. Math. Anal. 44(1):1?C60, 2012) the existence of a pure, global in time, soliton u(t) of the above equation was proved, satisfying $$\lim_{t\to -\infty}\|u(t) - Q_1(\cdot -(1-\lambda)t) \|_{H^1(\mathbb{R})} =0,\quad 0\leq \lambda<1,$$ provided ${\varepsilon}$ is small enough. Here R(t, x) := Q c (x ? (c ? ??)t) is the soliton of R t +? (R xx ??? R + R m ) x =?0. In addition, there exists ${\tilde \lambda \in (0,1)}$ such that, for all 0?<??? <?1 with ${\lambda\neq \tilde \lambda}$ , the solution u(t) satisfies $$\sup_{t\gg \frac{1}{\varepsilon}}\|u(t) - \kappa(\lambda)Q_{c_\infty}(\cdot-\rho(t)) \|_{H^1(\mathbb{R})}\lesssim \varepsilon^{1/2}.$$ Here ${{\rho'(t) \sim (c_\infty(\lambda) -\lambda)}}$ , with ${{\kappa(\lambda)=2^{-1/(m-1)}}}$ and ${{c_\infty(\lambda)>\lambda}}$ in the case ${0<\lambda<\tilde\lambda}$ (refraction), and ${\kappa(\lambda) =1}$ and c ??(??)?<??? in the case ${\tilde \lambda<\lambda<1}$ (reflection). In this paper we improve our preceding results by proving that the soliton is far from being pure as t ?? +???. Indeed, we give a lower bound on the defect induced by the potential a(·), for all ${{0<\lambda<1, \lambda\neq \tilde \lambda}}$ . More precisely, one has $$\liminf_{t\to +\infty}\| u(t) - \kappa_m(\lambda)Q_{c_\infty}(\cdot-\rho(t)) \|_{H^1(\mathbb{R})}>rsim \varepsilon^{1 +\delta},$$ for any ${{\delta>0}}$ fixed. This bound clarifies the existence of a dispersive tail and the difference with the standard solitons of the constant coefficients, gKdV equation. 相似文献
7.
I. I. Guseinov 《Few-Body Systems》2013,54(11):1773-1780
By the use of complete orthonormal sets of ${\psi ^{(\alpha^{\ast})}}$ -exponential type orbitals ( ${\psi ^{(\alpha^{\ast})}}$ -ETOs) with integer (for α * = α) and noninteger self-frictional quantum number α *(for α * ≠ α) in standard convention introduced by the author, the one-range addition theorems for ${\chi }$ -noninteger n Slater type orbitals ${(\chi}$ -NISTOs) are established. These orbitals are defined as follows $$\begin{array}{ll}\psi _{nlm}^{(\alpha^*)} (\zeta ,\vec {r}) = \frac{(2\zeta )^{3/2}}{\Gamma (p_l ^* + 1)} \left[{\frac{\Gamma (q_l ^* + )}{(2n)^{\alpha ^*}(n - l - 1)!}} \right]^{1/2}e^{-\frac{x}{2}}x^{l}_1 F_1 ({-[ {n - l - 1}]; p_l ^* + 1; x})S_{lm} (\theta ,\varphi )\\ \chi _{n^*lm} (\zeta ,\vec {r}) = (2\zeta )^{3/2}\left[ {\Gamma(2n^* + 1)}\right]^{{-1}/2}x^{n^*-1}e^{-\frac{x}{2}}S_{lm}(\theta ,\varphi ),\end{array}$$ where ${x=2\zeta r, 0<\zeta <\infty , p_l ^{\ast}=2l+2-\alpha ^{\ast}, q_l ^{\ast}=n+l+1-\alpha ^{\ast}, -\infty <\alpha ^{\ast} <3 , -\infty <\alpha \leq 2,_1 F_1 }$ is the confluent hypergeometric function and ${S_{lm} (\theta ,\varphi )}$ are the complex or real spherical harmonics. The origin of the ${\psi ^{(\alpha ^{\ast})} }$ -ETOs, therefore, of the one-range addition theorems obtained in this work for ${\chi}$ -NISTOs is the self-frictional potential of the field produced by the particle itself. The obtained formulas can be useful especially in the electronic structure calculations of atoms, molecules and solids when Hartree–Fock–Roothan approximation is employed. 相似文献
8.
The average of the moments for event shapes in e ?+? e??→hadrons within the context of next-to-leading order (NLO) perturbative QCD prediction in dispersive model is studied. Moments used in this article are $\langle {1-T}\rangle$ , $\langle \rho\rangle$ , $\langle {B_{\rm T}}\rangle$ and $\langle {B_{\rm W} }\rangle$ . We extract α s, the coupling constant in perturbative theory and α 0 in the non-perturbative theory using the dispersive model. By fitting the experimental data, the values of $\alpha_{\rm s} ({M_{\rm Z^0} })=0.1171\pm 0.00229$ and $\alpha_0 \left( {\mu_{\rm I} =2\,{\rm GeV}} \right)=0.5068\pm 0.0440$ are found. Our results are consistent with the above model. Our results are also consistent with those obtained from other experiments at different energies. All these features are explained in this paper. 相似文献
9.
We estimate $BR(K \to \pi \nu \bar \nu )$ in the context of the Standard Model by fitting for λ t≡V tdV ts * of the “kaon unitarity triangle” relation. To find the vertex of this triangle, we fit data from |? K|, the CP-violating parameter describing K mixing, and a ψ,K , the CP-violating asymmetry in B d 0 → J/ψK 0 decays, and obtain the values $\left. {BR(K \to \pi \nu \bar \nu )} \right|_{SM} = (7.07 \pm 1.03) \times 10^{ - 11} $ and $\left. {BR(K_L^0 \to \pi ^0 \nu \bar \nu )} \right|_{SM} = (2.60 \pm 0.52) \times 10^{ - 11} $ . Our estimate is independent of the CKM matrix element V cb and of the ratio of B-mixing frequencies ${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-0em} {\Delta m_{B_d } }}$ . We also use the constraint estimation of λ t with additional data from $\Delta m_{B_d } $ and |V ub|. This combined analysis slightly increases the precision of the rate estimation of $K^ + \to \pi ^ + \nu \bar \nu $ and $K_L^0 \to \pi ^0 \nu \bar \nu $ (by ?10 and ?20%, respectively). The measured value of $BR(K^ + \to \pi ^ + \nu \bar \nu )$ can be compared both to this estimate and to predictions made from ${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-0em} {\Delta m_{B_d } }}$ . 相似文献
10.
11.
D. V. Amelin E. B. Berdnikov S. I. Bityukov G. V. Borisov V. A. Dorofeev R. I. Dzhelyadin Yu. P. Gouz Yu. M. Ivanyushenkov I. A. Kachaev A. N. Karyukhin Yu. A. Khokhlov G. A. Klyuchnikov V. F. Konstantinov S. V. Kopikov M. E. Kostrikov V. V. Kostyukhin A. A. Kriushin T. A. Lomtadze V. D. Matveyev A. S. Mestvirishvili A. P. Ostankov D. I. Ryabchikov O. V. Solovyanov E. A. Starchenko E. G. Tskhadadze N. K. Vishnevsky E. V. Vlasov A. M. Zaitsev 《Zeitschrift fur Physik C Particles and Fields》1995,66(1-2):71-76
The decayf 1(1285)→ρ0(770)γ was studied at VES spectrometer of IHEP. Clear signal off 1(1285) is seen in the effective mass spectrum of the π+π?γ system in the reaction π?γN→π+π?π?γN at the momentum $P_{\pi ^ - } = 37 GeV/c$ . The branching fraction of decayf 1(1285)→ρ0(770)γ has been found to be $$BR(f_1 (1285) \to \rho ^0 (770)\gamma ) = (2.8 \pm 0.7(stat) \pm 0.6(syst)) \cdot 10^{ - 2} .$$ The ratio of the helicity amplitudes for ρ0 meson in its rest frame was determined by the analysis of angular distributions: $$\rho _{00} /\rho _{11} = 3.9 \pm 0.9(stat) \pm 1.0(syst).$$ 相似文献
12.
P. Weidenauer K. D. Duch M. Heel H. Kalinowsky F. Kayser E. Klempt B. May J. Reifenröther O. Schreiber M. Ziegler D. Bailey S. Barlag J. M. Butler U. Gastaldi R. Landua C. Sabev W. Dahme F. Feld-Dahme U. Schaefer W. R. Wodrich J. C. Bizot B. Delcourt J. Jeanjean H. Nguyen E. G. Auld D. A. Axen K. L. Erdman B. Howard R. Howard B. L. White S. Ahmad M. Comyn G. M. Marshall G. Beer L. P. Robertson M. Botlo C. Laa H. Vonach C. Amsler M. Doser J. Riedlberger U. Straumann P. Truöl ASTERIX Collaboration 《Zeitschrift fur Physik C Particles and Fields》1990,47(3):353-365
We have measured the branching ratios for \(\bar pp\) annihilation at rest intoπ + π ? η andπ + π ? η′ in hydrogen gas in two data samples that have different fractions ofS-wave andP-wave initial states. The branching ratios are derived from a comparison with the topological branching ratio for \(\bar pp\) annihilations into four charged pions of (49±4)% and the branching ratio intoπ + π ? π + π ? π 0 of (18.7±1.6)%. We find a significant reduction of the branching ratios fromP-states for \(\bar pp \to \pi ^ + \pi ^ - \eta \) andπ + π ? η′ in comparison toS-state annihilation. $$\begin{gathered} BR(S - wave \to \pi ^ + \pi ^ - \eta ) = (13.7 \pm 1.46) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to \pi ^ + \pi ^ - \eta ) = (3.35 \pm 0.84) \cdot 10^{ - 3} \hfill \\ BR(S - wave \to \pi ^ + \pi ^ - \eta ') = (3.46 \pm 0.67) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to \pi ^ + \pi ^ - \eta ') = (0.61 \pm 0.33) \cdot 10^{ - 3} . \hfill \\ \end{gathered} $$ In a partial wave analysis of theπ + π ? η Dalitz plot we find the following contributions: Phase space, \(a_2^ + (1320)\pi ^ \mp \) ,ηρ0 andf 2(1270)η: $$\begin{gathered} BR(S - wave \to \pi ^ + \pi ^ - \eta PS) = (6.31 \pm 1.22) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to \pi ^ + \pi ^ - \eta PS) = (0.47 \pm 0.26) \cdot 10^{ - 3} \hfill \\ BR(^1 S_0 \to a_2^ \pm (1320)\pi ^ \mp ) = (2.59 \pm 0.73) \cdot 10^{ - 3} \hfill \\ BR(^3 S_1 \to a_2^ \pm (1320)\pi ^ \mp ) = (1.31 \pm 0.48) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to a_2^ \pm (1320)\pi ^ \mp ) = (1.31 \pm 0.69) \cdot 10^{ - 3} \hfill \\ BR(^3 S_1 \to \rho \eta ) = (3.29 \pm 0.90) \cdot 10^{ - 3} \hfill \\ BR(^1 P_1 \to \rho \eta ) = (0.94 \pm 0.53) \cdot 10^{ - 3} \hfill \\ BR(^1 S_0 \to f_2 (1270)\eta ) = (0.083 \pm 0.086) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to f_2 (1270)\eta ) = (0.64 \pm 0.26) \cdot 10^{ - 3} . \hfill \\ \end{gathered} $$ We find a 2 σ effect for the reaction \(\bar pp \to a_0^ \pm (980)\pi ^ \mp \) , \(a_0^ \pm \to \eta \pi ^ \pm \) , with a branching ratio of (0.13±0.07)·10?3. For η' production we give a branching ratio of \(\bar pp \to \rho \eta '\) of (1.81±0.44)·10?3 from3 S 1. We estmate a contribution of about 0.3·10?3 for ρη' fromP-states. The ratio of ρη and ρη' rpoduction is used to test the validity of the quark line rule. In theπ + π ? π + π ? γ final state we do not observe the reaction \(\bar pp \to \pi ^ + \pi ^ - \omega \) , ω→π + π ? λ and derive an upper limit of 3·10?3 for decay modeω→π + π ? λ. 相似文献
13.
We prove a regularity result in weighted Sobolev (or Babu?ka?CKondratiev) spaces for the eigenfunctions of certain Schr?dinger-type operators. Our results apply, in particular, to a non-relativistic Schr?dinger operator of an N-electron atom in the fixed nucleus approximation. More precisely, let ${\mathcal{K}_{a}^{m}(\mathbb{R}^{3N},r_S)}$ be the weighted Sobolev space obtained by blowing up the set of singular points of the potential ${V(x) = \sum_{1 \le j \le N} \frac{b_j}{|x_j|} + \sum_{1 \le i < j \le N} \frac{c_{ij}}{|x_i-x_j|}}$ , ${x \in \mathbb{R}^{3N}}$ , ${b_j, c_{ij} \in \mathbb{R}}$ . If ${u \in L^2(\mathbb{R}^{3N})}$ satisfies ${(-\Delta + V) u = \lambda u}$ in distribution sense, then ${u \in \mathcal{K}_{a}^{m}}$ for all ${m \in \mathbb{Z}_+}$ and all a ?? 0. Our result extends to the case when b j and c ij are suitable bounded functions on the blown-up space. In the single-electron, multi-nuclei case, we obtain the same result for all a?<?3/2. 相似文献
14.
T. F. Hoang 《Zeitschrift fur Physik C Particles and Fields》1991,49(2):311-316
The rapidity distributions of inclusive \(e^ + e^ - \to h\bar h + \cdot \cdot \cdot\) of PEP and DESY experiments are analyzed in terms of the covariant partition temperatureT p model. The estimates ofT p * in the fireball system are comparable to the conventional temperature, the energy dependence follows approximately Stefan's law, the radius of the specific volume ralative to the energy density being ~1.18 fm. In the c.m.s. of collision, \(T_p = AW^a (W = \sqrt s in GeV)\) witha=0.60±0.05 andA=0.256±0.006, it is found \(T_p \cong {W \mathord{\left/ {\vphantom {W {\tfrac{3}{2}\left\langle {n_ \pm } \right\rangle }}} \right. \kern-0em} {\tfrac{3}{2}\left\langle {n_ \pm } \right\rangle }}\) . These properties hold also for \(\bar pp\) collision, but not forpp→π?+... 相似文献
15.
Zhi-Gang Wang 《The European Physical Journal C - Particles and Fields》2010,68(3-4):479-486
In this article, we study the masses and pole residues of the ${1\over2}^{\pm}$ flavor antitriplet heavy baryon states ( $\varLambda _{c}^{+}$ , $\varXi _{c}^{+},\varXi _{c}^{0})$ and ( $\varLambda _{b}^{0}$ , $\varXi _{b}^{0},\varXi _{b}^{-})$ by subtracting the contributions from the corresponding ${1\over2}^{\mp}$ heavy baryon states with the QCD sum rules, and observe that the masses are in good agreement with the experimental data and make reasonable predictions for the unobserved ${1\over2}^{-}$ bottom baryon states. Once reasonable values of the pole residues λ Λ and λ Ξ are obtained, we can take them as basic parameters to study the relevant hadronic processes with the QCD sum rules. 相似文献
16.
László Erdős Antti Knowles Horng-Tzer Yau Jun Yin 《Communications in Mathematical Physics》2013,323(1):367-416
We consider Hermitian and symmetric random band matrices H = (h xy ) in ${d\,\geqslant\,1}$ d ? 1 dimensions. The matrix entries h xy , indexed by ${x,y \in (\mathbb{Z}/L\mathbb{Z})^d}$ x , y ∈ ( Z / L Z ) d , are independent, centred random variables with variances ${s_{xy} = \mathbb{E} |h_{xy}|^2}$ s x y = E | h x y | 2 . We assume that s xy is negligible if |x ? y| exceeds the band width W. In one dimension we prove that the eigenvectors of H are delocalized if ${W\gg L^{4/5}}$ W ? L 4 / 5 . We also show that the magnitude of the matrix entries ${|{G_{xy}}|^2}$ | G x y | 2 of the resolvent ${G=G(z)=(H-z)^{-1}}$ G = G ( z ) = ( H - z ) - 1 is self-averaging and we compute ${\mathbb{E} |{G_{xy}}|^2}$ E | G x y | 2 . We show that, as ${L\to\infty}$ L → ∞ and ${W\gg L^{4/5}}$ W ? L 4 / 5 , the behaviour of ${\mathbb{E} |G_{xy}|^2}$ E | G x y | 2 is governed by a diffusion operator whose diffusion constant we compute. Similar results are obtained in higher dimensions. 相似文献
17.
LetS ?=??Δ+V, withV smooth. If 0<E 2V(x), the spectrum ofS ? nearE 2 consists (for ? small) of finitely-many eigenvalues,λ j (?). We study the asymptotic distribution of these eigenvalues aboutE 2 as ?→0; we obtain semi-classical asymptotics for $$\sum\limits_j {f\left( {\frac{{\sqrt {\lambda _j (\hbar )} - E}}{\hbar }} \right)} $$ with \(\hat f \in C_0^\infty \) , in terms of the periodic classical trajectories on the energy surface \(B_E = \left\{ {\left| \xi \right|^2 + V(x) = E^2 } \right\}\) . This in turn gives Weyl-type estimates for the counting function \(\# \left\{ {j;\left| {\sqrt {\lambda _j (\hbar )} - E} \right| \leqq c\hbar } \right\}\) . We make a detailed analysis of the case when the flow onB E is periodic. 相似文献
18.
Walter Craig 《Communications in Mathematical Physics》1983,88(1):113-131
The finite difference Schrödinger operator on ? m is considered $$Hu_j = \left( {\sum\limits_{v = 1}^m { D_v^2 } } \right)u_j + \frac{1}{\varepsilon }q_j u_j ,u \in \ell ^2 (\mathbb{Z}^m ),$$ where \(\sum\limits_{v = 1}^m { D_v^2 } \) is the difference Laplacian inm dimensions. For ? sufficiently small almost periodic potentialsq j are constructed such that the operatorH has only pure point spectrum. The method is an inverse spectral procedure, which is a modification of the Kolmogorov-Arnol'd-Moser technique. 相似文献
19.
Sorin Popa 《Communications in Mathematical Physics》2014,332(1):379-414
We show that the Kadison–Singer problem, asking whether the pure states of the diagonal subalgebra \({\ell^\infty\mathbb{N}\subset \mathcal{B}(\ell^2\mathbb{N})}\) have unique state extensions to \({\mathcal{B}(\ell^2\mathbb{N})}\) , is equivalent to a similar statement in II1 factor framework, concerning the ultrapower inclusion \({D^\omega \subset R^\omega}\) , where D is the Cartan subalgebra of the hyperfinite II1 factor R (i.e., a maximal abelian *-subalgebra of R whose normalizer generates R, e.g. \({D=L^\infty([0, 1]^{\mathbb{Z}}) \subset L^\infty([0,1]^{\mathbb{Z}} \rtimes \mathbb{Z} = R)}\) , and ω is a free ultrafilter. Instead, we prove here that if A is any singular maximal abelian *-subalgebra of R (i.e., whose normalizer consists of the unitary group of A, e.g. \({A=L(\mathbb{Z})\subset L^\infty([0,1]^\mathbb{Z})\rtimes \mathbb{Z}=R}\) ), then the inclusion \({A^\omega \subset R^\omega}\) does satisfy the Kadison–Singer property. 相似文献
20.
For every unconditionally convergent series $\sum_{j=1}^{\infty}x_{j}$ in sequentially complete Abelian topological group, we show that the sum $\sum_{j=1}^{\infty}x_{\theta(j)}$ is same for all permutations θ:?→?. This result justify the measures defined on quantum structures. 相似文献