共查询到20条相似文献,搜索用时 566 毫秒
1.
Let B(H) be the bounded operators on a Hilbert space H. A linear subspace R ? B(H) is said to be an operator system if 1 ?R and R is self-adjoint. Consider the category of operator systems and completely positive linear maps. R ∈ is said to be injective if given A ? B, A, B ∈ , each map A → R extends to B. Then each injective operator system is isomorphic to a conditionally complete C1-algebra. Injective von Neumann algebras R are characterized by any one of the following: (1) a relative interpolation property, (2) a finite “projectivity” property, (3) letting Mm = B(Cm), each map R → N ? Mm has approximate factorizations R → Mn → N, (4) letting K be the orthogonal complement of an operator system N ? Mm, each map has approximate factorizations . Analogous characterizations are found for certain classes of C1-algebras. 相似文献
2.
Robert Bantegnie 《Journal of Number Theory》1974,6(2):73-98
The “cylinder conjecture” is to suppose that, if K is a gauge, the critical constants of C(K) = K ×] ? 1, +1 [? Rn+1 and of its basis K ? Rn are equal. The connection with packing constants is studied. The concept of Za(ssenhaus)-packing is introduced. ⊕i=1hG + (i ? 1)a (G a lattice) is a linear h-lattice, , the maximum density for translates of K by a linear h-lattice if the translates form a Za-packing for ζ, a packing for η, and if this packing is strict for ^. For K a bounded central star body, it is possible to find H with ζ1(C(K)) ≤ 2 ζH′(K). H is precised for K a gauge and for K = Bn. It is proved by Woods' methods that ; a result of Cleaver is used. 相似文献
3.
Loren D. Pitt 《Journal of multivariate analysis》1978,8(1):45-54
For Gaussian vector fields {X(t) ∈ Rn:t ∈ Rd} we describe the covariance functions of all scaling limits Y(t) = limα↓0 B?1(α) X(αt) which can occur when B(α) is a d × d matrix function with B(α) → 0. These matrix covariance functions are found to be homogeneous in the sense that for some matrix L and each α > 0, . Processes with stationary increments satisfying (1) are further analysed and are found to be natural generalizations of Lévy's multiparameter Brownian motion. 相似文献
4.
Ivan Singer 《Journal of Mathematical Analysis and Applications》1980,76(2):339-368
We show that, if (F →uX) is a linear system, a convex target set and a convex functional, then, under suitable assumptions, the computation of inf ) can be reduced to the computation of the infimum of h on certain strips or hyperplanes in F, determined by elements of , or of the infima on F of Lagrangians, involving elements of . Also, we prove similar results for a convex system (F →uX) and the convex cone Ω of all non-positive elements in X. 相似文献
5.
A.G Ramm 《Journal of Mathematical Analysis and Applications》1984,98(1):92-98
Consider the exterior boundary value problem (▽2 + K2) u = 0, in Ω, k >0. , where Γ is a smooth closed connected surface in 3, , ∝ is called the radiation pattern. We prove that when h runs through any dense set in L2(Γ) the corresponding radiation pattern ∝(k,n) runs through a dense set in L2(S2) for any k >0, where S2 is the unit sphere in 3. 相似文献
6.
Variational problems for the multiple integral , where and are studied. A new condition on g, called W1,p-quasiconvexity is introduced which generalizes in a natural way the quasiconvexity condition of C. B. Morrey, it being shown in particular to be necessary for sequential weak lower semicontinuity of in and for the existence of minimizers for certain related integrals. Counterexamples are given concerning the weak continuity properties of Jacobians in , p ? n = m. An existence theorem for nonlinear elastostatics is proved under optimal growth hypotheses. 相似文献
7.
A regularity result for singular nonlinear elliptic systems in inverse-power weighted Sobolev spaces
P.D Smith 《Journal of Differential Equations》1984,53(2):125-138
The compactness method to weighted spaces is extended to prove the following theorem:Let H2,s1(B1) be the weighted Sobolev space on the unit ball in Rn with norm Let n ? 2 ? s < n. Let u? [H2,s1(B1) ∩ L∞(B1)]N be a solution of the nonlinear elliptic system , are uniformly continuous functions of their arguments and satisfy: . Then there exists an R1, 0 < R1 < 1, and an α, 0 < α < 1, along with a set such that (1) , (2) Ω does not contain the origin; Ω does not contain BR1, (3) is open, (4) u is ; u is LipαBR1. 相似文献
8.
Wolfgang Wasow 《Linear algebra and its applications》1977,18(2):163-170
Let A(x,ε) be an n×n matrix function holomorphic for |x|?x0, 0<ε?ε0, and possessing, uniformly in x, an asymptotic expansion , as ε→0+. An invertible, holomorphic matrix function P(x,ε) with an asymptotic expansion , as ε→0+, is constructed, such that the transformation y = P(x,ε)z takes the differential equation a positive integer, into , where B(x,ε) is asymptotically equal, to all orders, to a matrix in a canonical form for holomorphic matrices due to V.I. Arnold. 相似文献
9.
Minoru Murata 《Journal of Functional Analysis》1984,56(3):300-310
Let H = ?Δ + V, where V is a multiplication operator by a real-valued function V(x) on Rn which is uniformly Hölder continuous and for some ? > 4. The relationship between existence of positive solutions, with growth conditions, of Hg = 0 and asymptotic behaviors as t → ∞ of e?th is established. Using it B. Simon's problem for H on R2 is solved. 相似文献
10.
Georg Lindgren 《Journal of multivariate analysis》1980,10(2):181-206
Let ζ(t), η(t) be continuously differentiable Gaussian processes with mean zero, unit variance, and common covariance function r(t), and such that ζ(t) and η(t) are independent for all t, and consider the movements of a particle with time-varying coordinates (ζ(t), η(t)). The time and location of the exists of the particle across a circle with radius u defines a point process in R3 with its points located on the cylinder {(t, u cos θ, u sin θ); t ≥ 0, 0 ≤ θ < 2π}. It is shown that if r(t) log t → 0 as t → ∞, the time and space-normalized point process of exits converges in distribution to a Poisson process on the unit cylinder. As a consequence one obtains the asymptotic distribution of the maximum of a χ2-process, χ2(t) = ζ2(t) + η2(t), P{sup0≤t≤Tχ2(t) ≤ u2} → e?τ if as T, u → ∞. Furthermore, it is shown that the points in R3 generated by the local ?-maxima of χ2(t) converges to a Poisson process in R3 with intensity measure (in cylindrical polar coordinates) (2πr2)?1dtdθdr. As a consequence one obtains the asymptotic extremal distribution for any function g(ζ(t), η(t)) which is “almost quadratic” in the sense that has a limit as r → ∞. Then if as T, u → ∞. 相似文献
11.
Tomas Schonbek 《Journal of Differential Equations》1985,56(2):290-296
New and more elementary proofs are given of two results due to W. Littman: (1) Let . The estimate cannot hold for all u?C0∞(Q), Q a cube in , some constant C. (2) Let n ? 2, p ≠ 2. The estimate cannot hold for all C∞ solutions of the wave equation □u = 0 in ; all t ?; some function C: → . 相似文献
12.
Simon Wassermann 《Journal of Functional Analysis》1976,23(3):239-254
If A and B are C1-algebras there is, in general, a multiplicity of C1-norms on their algebraic tensor product A ⊙ B, including maximal and minimal norms ν and α, respectively. A is said to be nuclear if α and ν coincide, for arbitrary B. The earliest example, due to Takesaki [11], of a nonnuclear C1-algebra was , the C1-algebra generated by the left regular representation of the free group on two generators F2. It is shown here that W1-algebras, with the exception of certain finite type I's, are nonnuclear.If is the group C1-algebra of F2, there is a canonical homomorphism λl of onto . The principal result of this paper is that there is a norm ζ on , distinct from α, relative to which the homomorphism is bounded ( being endowed with the norm α). Thus quotients do not, in general, respect the norm α; a consequence of this is that the set of ideals of the α-tensor product of C1-algebras A and B may properly contain the set of product ideals {}.Let A and B be C1-algebras. If A or B is a W1-algebra there are on A ⊙ B certain C1-norms, defined recently by Effros and Lance [3], the definitions of which take account of normality. In the final section of the paper it is shown by example that these norms, with α and ν, can be mutually distinct. 相似文献
13.
Harry Dym 《Journal of Functional Analysis》1978,28(1):33-57
Let PT denote the orthogonal projection of L2(R1, dΔ) onto the space of entire functions of exponential type ? T which are square summable on the line with respect to the measure , and let G denote the operator of multiplication by a suitably restricted complex valued function g. It is shown that if is summable, if is locally summable, and if belongs to the span in L∞ of e?iyTH∞:T ? 0, in which h is chosen to be an outer function and h#(γ) agrees with the complex conjugate of h(γ) on the line, then exists and is independent of h for every positive integer n. This extends the range of validity of a formula due to Mark Kac who evaluated this limit in the special case h = 1 using a different formalism. It also extends earlier results of the author which were established under more stringent conditions on h. The conclusions are based in part upon a preliminary study of a more general class of projections. 相似文献
14.
Let be the n-dimensional ice cream cone, and let Γ(Kn) be the cone of all matrices in nn mapping Kn into itself. We determine the structure of Γ(Kn), and in particular characterize the extreme matrices in Γ(Kn). 相似文献
15.
Ramzi May 《Comptes Rendus Mathematique》2003,336(9):731-734
Let be a maximal solution of the Navier–Stokes equations. We prove that u is C∞ on and there exists a constant , which depends only on n, such that if is finite then, for all we have To cite this article: R. May, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
16.
Detlef Müller 《Journal of Functional Analysis》1982,47(2):247-280
Let F1(Rn) denote the Fourier algebra on n, and (n) the space of test functions on n. A closed subset E of n is said to be of spectral synthesis if the only closed ideal J in F1(Rn) which has E as its hull is the ideal . We consider sufficiently regular compact subsets of smooth submanifolds of n with constant relative nullity. For such sets E we give an estimate of the degree of nilpotency of the algebra , where j(E) denotes the smallest closed ideal in F1(Rn) with hull E. Especially in the case of hypersurfaces this estimate turns out to be exact. Moreover for this case we prove that k(E)∩D(Rn) is dense in k(E). Together this solves the synthesis problem for such sets. 相似文献
17.
《Nonlinear Analysis: Theory, Methods & Applications》2004,56(5):781-791
We consider the equation −Δu+V(x)u=f(x,u) for where is a positive potential bounded away from zero, and the nonlinearity behaves like exp(α|u|2) as |u|→∞. We also assume that the potential V(x) and the nonlinearity f(x,u) are asymptotically periodic at infinity. We prove the existence of at least one weak positive solution by combining the mountain-pass theorem with Trudinger–Moser inequality and a version of a result due to Lions for critical growth in . 相似文献
18.
Boguslaw Tomaszewski 《Journal of Functional Analysis》1984,55(1):63-67
It is shown, for n ? m ? 1, that there exist inner maps Φ: Bn → Bm with boundary values such that . where σn and σm are the Haar measures on ?Bn and ?Bm, respectively, and A ? Bn is an arbitrary Borel set. 相似文献
19.
Woody Lichtenstein 《Journal of Functional Analysis》1979,34(3):433-455
For a symmetric space of compact type, the highest-weight vectors for representations of G occurring in become heavily concentrated near certain submanifolds of as the highest weight goes to infinity. This fact is applied to obtain estimates for the spectral measures of the operators qλ = PλqPλ, where is an orthogonal projection onto a G-irreducible summand, and q: G/K → is a continuous function acting on by multiplication. 相似文献
20.
W Fernandez de la Vega 《Journal of Combinatorial Theory, Series B》1983,35(3):328-332
For any tournament T on n vertices, let h(T) denote the maximum number of edges in the intersection of T with a transitive tournament on the same vertex set. Sharpening a previous result of Spencer, it is proved that, if Tn denotes the random tournament on n vertices, then, as n → ∞. 相似文献