共查询到20条相似文献,搜索用时 31 毫秒
1.
Palle E.T Jørgensen 《Journal of Functional Analysis》1982,45(3):341-356
We consider unbounded 1-derivations δ in UHF-C1-algebras A=(∪∞n=1An)?) with dense domain. If ?n:A→An denotes the conditional expectations onto the finite type I factors n, then we introduce a weak-commutativity condition for δ and the sequence (?n). As a consequence of this condition on δ we establish the existence of an extension derivation δ′ which is the infinitesimal generator of a strongly continuous one-parameter group, α: → Aut(), of 1-automorphisms, i.e., for x?D(δ′). Special properties of α (alias δ′) are considered. We show that AF-algebras are associated to proper restrictions δ of derivations δ′ of product type. We then turn to the extendability problem for quasifree derivations in the CAR-algebra. There, extensions δ′ are calculated which generate strongly continuous semigroups of 1-homomorphisms. These semigroups do not extend to one-parameter groups unless the implementing symmetric operator in one-particle space is already self-adjoint. 相似文献
2.
Ola Bratteli Frederick M Goodman Palle E.T Jørgensen 《Journal of Functional Analysis》1985,61(3):247-289
Let G be a compact abelian group, and τ an action of G on a C1-algebra , such that τ(γ)τ(γ)1 = τ(0) τ for all , where τ(γ) is the spectral subspace of corresponding to the character γ on G. Derivations δ which are defined on the algebra F of G-finite elements are considered. In the special case δ¦τ = 0 these derivations are characterized by a cocycle on with values in the relative commutant of τ in the multiplier algebra of , and these derivations are inner if and only if the cocycles are coboundaries and bounded if and only if the cocycles are bounded. Under various restrictions on G and τ properties of the cocycle are deduced which again give characterizations of δ in terms of decompositions into generators of one-parameter subgroups of τ(G) and approximately inner derivations. Finally, a perturbation technique is devised to reduce the case δ(F) ? F to the case δ(F) ? F and δ¦τ = 0. This is used to show that any derivation δ with D(δ) = F is wellbehaved and, if furthermore G = T1 and δ(F) ? F the closure of δ generates a one-parameter group of 1-automorphisms of . In the case G = Td, d = 2, 3,… (finite), and δ(F) ? F it is shown that δ extends to a generator of a group of 1-automorphisms of the σ-weak closure of in any G-covariant representation. 相似文献
3.
Let H and K be symmetric linear operators on a C1-algebra with domains D(H) and D(K). H is defined to be strongly K-local if implies for A?D(H) ∩ D(K) and ω in the state space of , and H is completely strongly K-local if implies for A ∈ D(H) ∩ D(K) and Ω in the state of , and H is cpmpletely strongly K-local if is -local on U?Mn for all n ? 1, where n is the identity on the n × n matrices Mn. If is abelian then strong locality and complete strong locality are equivalent. The main result states that if τ is a strongly continuous one-parameter group of 1-automorphisms of with generator δ0 and δ is a derivation which commutes with τ and is completely strongly δ0-local then δ generates a group α of 1-automorphisms of . Various characterizations of α are given and the particular case of periodic τ is discussed. 相似文献
4.
Chan-nan Chang 《Journal of Number Theory》1973,5(6):456-476
Let L be a lattice over the integers of a quaternion algebra with center K which is a -adic field. Then the unitary group U(L) equals its own commutator subgroup and is generated by the unitary transvections and quasitransvections contained in it. Let g be a tableau, U(g), U+(g), , T(g) be the corresponding congruence subgroups of order g. Then , and (the subgroup generated by the unitary transvections and quasitransvections with order ≤ g). Let G be a subgroup of U(L) with o(G) = g, then G is normal in U(L) if and only if U(g) ? G ? T(g). 相似文献
5.
Alan L.T Paterson 《Journal of Functional Analysis》1983,53(3):203-223
A theory of harmonic analysis on a metric group (G, d) is developed with the model of U, the unitary group of a C1-algebra , in mind. Essential in this development is the set of contractive, irreducible representations of G, and its concomitant set Pd(G) of positive-definite functions. It is shown that is compact and closed in . The set is determined in a number of cases, in particular when G = U() with abelian. If is an AW1-algebra, it is shown that d is essentially the same as . Unitary groups are characterised in terms of a certain Lie algebra u and several characterisations of G = U() when is abelian are given. 相似文献
6.
Let G be a bounded domain in such that is strictly pseudoconvex and U an open subset of bG. We define an open subset of with the property such that the following extension theorem holds true: for every ?∈C(U) there exist two functions such that Φ±|U=? and the graphs Γ(Φ±) of Φ± are Levi-flat over . Moreover, for each such that Φ|U=? and Γ(Φ) is Levi-flat over one has Φ??Φ?Φ+ on . We also show that if G is diffeomorphic to a 3-ball and U is the union of simply-connected domains each of which is contained either in the “upper” or in the “lower” part of bG (with respect to the u-direction), then is the maximal domain of Levi-flat extensions for some function ?∈C(U). To cite this article: N. Shcherbina, G. Tomassini, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
7.
Explicit and asymptotic solutions are presented to the recurrence M(1) = g(1), M(n + 1) = g(n + 1) + min1 ? t ? n(αM(t) + βM(n + 1 ? t)) for the cases (1) α + β < 1, is rational, and g(n) = δnI. (2) α + β > 1, min(α, β) > 1, is rational, and (a) g(n) = δn1, (b) g(n) = 1. The general form of this recurrence was studied extensively by Fredman and Knuth [J. Math. Anal. Appl.48 (1974), 534–559], who showed, without actually solving the recurrence, that in the above cases , where γ is defined by α?γ + β?γ = 1, and that does not exist. Using similar techniques, the recurrence M(1) = g(1), M(n + 1) = g(n + 1) + max1 ? t ? n(αM(t) + βM(n + 1 ? t)) is also investigated for the special case α = β < 1 and g(n) = 1 if n is odd = 0 if n is even. 相似文献
8.
Alan McIntosh 《Journal of Functional Analysis》1978,30(2):264-275
It is shown that there is a closed symmetric derivation δ of a C1-algebra with dense domain (δ), an element A = A1 ?(δ), and a C1-function such that (A)?(δ). Some estimates are derived for , where 0 < α < 1. It is shown that there exists a family of one-one self-adjoint operators S(t) in (H) which depends linearly on t, while is not differentiable. It is also shown that there exists (H) which is not C1-self-adjoint even though it satisfies for all t ? 相似文献
9.
Harry Dym 《Journal of Functional Analysis》1979,31(1):69-100
In this paper we study trace formulas for a class of operators of the form ΠT-GΠT in which G designates multiplication by a suitable restricted d × d matrix valued function G(γ) of γ?R1and ΠT stands for the diagonal d × d matrix (δijPT) of orthogonal projections PT of L2(R1, dδ) onto the space IT(dδ) of entire functions of exponential type ?T which are square summable on the line relative to the measure . It is shown that, for a reasonably large class of h, exists and is independent of the choice of h within the permitted class. These results are then used to study the asymptotic behavior, as T ↑ ∞, of the determinant of I ? ΠTGΠT. 相似文献
10.
Teruo Ikebe 《Journal of Functional Analysis》1975,20(2):158-177
A spectral representation for the self-adjoint Schrödinger operator H = ?Δ + V(x), x? R3, is obtained, where V(x) is a long-range potential: , grad , being the Laplace-Beltrami operator on the unit sphere Ω. Namely, we shall construct a unitary operator from PL2(R3) onto being the orthogonal projection onto the absolutely continuous subspace for H, such that for any Borel function α(λ), . 相似文献
11.
CAI Mao-cheng 《Discrete Mathematics》1984,49(1):15-20
Given a finite loopless graph G (resp. digraph D), let σ(G), ?(G) and ψ(D) denote the minimal cardinalities of a completely separating system of G, a separating system of G and a separating system of D, respectively. The main results of this paper are: denotes the chromatic number of G. (ii) All the problems of determining σ(G), ?(G) and ψ(D) are NP-complete. 相似文献
12.
Tom Brylawski 《Discrete Mathematics》1977,18(3):243-252
In “The Slimmest Geometric Lattices” (Trans. Amer. Math. Soc.). Dowling and Wilson showed that if G is a combinatorial geometry of rank r(G) = n, and if X(G) = Σμ(0, x)λr ? r(x) = Σ (?1)r ? kWkλk is the characteristic polynomial of G, then Thus γ(G) ? 2r ? 1 (n+2), where γ(G) = Σwk. In this paper we sharpen these lower bounds for connected geometries: If G is connected, r(G) ? 3, and n(G) ? 2 ((r, n) ≠ (4,3)), then |μ| ? (r? 1)n; and γ ? (2r ? 1 ? 1)(2n + 2). These bounds are all achieved for the parallel connection of an r-point circuit and an (n + 1)point line. If G is any series-parallel network, , and then . Further, if β is the Crapo invariant, then β(G) ? max(1, n ? r + 2). This lower bound is achieved by the parallel connection of a line and a maximal size series-parallel network. 相似文献
13.
Let (, G, α) be a dynamical system and let δ be a closed 1 derivation in which commutes with α and satisfies G ? ker(δ). If is a separable Type I algebra and G is a second countable compact group, then δ generates a strongly continuous one parameter group of 1 automorphisms of . 相似文献
14.
Chungming An 《Journal of Number Theory》1974,6(1):1-6
A Dirichlet series associated with a positive definite form of degree δ in n variables is defined by where ? ∈ , α ∈ n, 〈x, y〉 = x1y1 + ? + xnyn, e(a) = exp (2πia) for a ∈ , and s = σ + ti is a complex number. The author proves that: (1) DF(s, ?, α) has analytic continuation into the whole s-plane, (2) DF(s, ?, α), ? ≠ 0, is a meromorphic function with at most a simple pole at . The residue at is given explicitly. (3) ? = 0, α ? n, DF(s, 0, α) is analytic for . 相似文献
15.
Best upper and lower bounds, as functions of n, are obtained for the quantities and , where β2(G) denotes the total matching number and α2(G) the total covering number of any graph G with n vertices and with complementry graph ?.The best upper bound is obtained also for α2(G)+β2(G), when G is a connected graph. 相似文献
16.
17.
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
18.
19.
The group ring R(G) of a group G over a coefficient ring R is well known and so is the L1 group algebra . We study in this note . where R is Zp(Qp) the ring (field) of p-adic integers (numbers) equipped with the p-adic valuation. Analogues of certain well known results for group rings and l1(G) are obtained for l(R,G). 相似文献