共查询到20条相似文献,搜索用时 62 毫秒
1.
Ruy Exel 《Journal of Functional Analysis》2003,199(1):153-188
Given a unital -algebra A, an injective endomorphism preserving the unit, and a conditional expectation E from A to the range of α we consider the crossed-product of A by α relative to the transfer operator L=α−1E. When E is of index-finite type we show that there exists a conditional expectation G from the crossed-product to A which is unique under certain hypothesis. We define a “gauge action” on the crossed-product algebra in terms of a central positive element h and study its KMS states. The main result is: if h>1 and E(ab)=E(ba) for all a,b∈A (e.g. when A is commutative) then the KMSβ states are precisely those of the form ψ=φ°G, where φ is a trace on A satisfying the identity
2.
We investigate if, for a locally compact group G, the Fourier algebra A(G) is biflat in the sense of quantized Banach homology. A central rôle in our investigation is played by the notion of an approximate indicator of a closed subgroup of G: The Fourier algebra is operator biflat whenever the diagonal in G×G has an approximate indicator. Although we have been unable to settle the question of whether A(G) is always operator biflat, we show that, for , the diagonal in G×G fails to have an approximate indicator. 相似文献
3.
G.K. Eleftherakis 《Journal of Pure and Applied Algebra》2008,212(5):1060-1071
We generalize the main theorem of Rieffel for Morita equivalence of W∗-algebras to the case of unital dual operator algebras: two unital dual operator algebras A,B have completely isometric normal representations α,β such that α(A)=[M∗β(B)M]−w∗ and β(B)=[Mα(A)M∗]−w∗ for a ternary ring of operators M (i.e. a linear space M such that MM∗M⊂M) if and only if there exists an equivalence functor which “extends” to a ∗-functor implementing an equivalence between the categories and . By we denote the category of normal representations of A and by the category with the same objects as and Δ(A)-module maps as morphisms (Δ(A)=A∩A∗). We prove that this functor is equivalent to a functor “generated” by a B,A bimodule, and that it is normal and completely isometric. 相似文献
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5.
Tomoyoshi Ohwada 《Journal of Functional Analysis》2005,222(2):274-291
Let (M,α,G) be a covariant system on a locally compact Abelian group G with the totally ordered dual group which admits the positive semigroup . Let H∞(α) be the associated analytic subalgebra of M; i.e. . Let be the analytic crossed product determined by a covariant system . We give the necessary and sufficient condition that an analytic subalgebra H∞(α) is isomorphic to an analytic crossed product related to Landstad's theorem. We also investigate the structure of σ-weakly closed subalgebra of a continuous crossed product N?θR which contains N?θR+. We show that there exists a proper σ-weakly closed subalgebra of N?θR which contains N?θR+ and is not an analytic crossed product. Moreover we give an example that an analytic subalgebra is not a continuous analytic crossed product using the continuous decomposition of a factor of type IIIλ(0?λ<1). 相似文献
6.
Zhi-Hong Sun 《Discrete Mathematics》2008,308(1):71-112
Let {Bn(x)} be the Bernoulli polynomials. In the paper we establish some congruences for , where p is an odd prime and x is a rational p-integer. Such congruences are concerned with the properties of p-regular functions, the congruences for and the sum , where h(d) is the class number of the quadratic field of discriminant d and p-regular functions are those functions f such that are rational p-integers and for n=1,2,3,… . We also establish many congruences for Euler numbers. 相似文献
7.
Non-linear numerical radius isometries on atomic nest algebras and diagonal algebras 总被引:1,自引:0,他引:1
A nonlinear map φ between operator algebras is said to be a numerical radius isometry if w(φ(T−S))=w(T−S) for all T, S in its domain algebra, where w(T) stands for the numerical radius of T. Let and be two atomic nests on complex Hilbert spaces H and K, respectively. Denote the nest algebra associated with and the diagonal algebra. We give a thorough classification of weakly continuous numerical radius isometries from onto and a thorough classification of numerical radius isometries from onto . 相似文献
8.
《Advances in Mathematics》2004,182(2):278-306
Let Tα be the translation operator by α in the space of entire functions defined by . We prove that there is a residual set G of entire functions such that for every f∈G and every the sequence is dense in , that is, G is a residual set of common hypercyclic vectors ( functions) for the family . Also, we prove similar results for many families of operators as: multiples of differential operator, multiples of backward shift, weighted backward shifts. 相似文献
9.
We estimate the norm of the almost Mathieu operator , regarded as an element in the rotation C*-algebra . In the process, we prove for every λ∈R and the inequality
10.
We consider the following question: given A∈SL(2,R), which potentials q for the second order Sturm-Liouville problem have A as its Floquet multiplier? More precisely, define the monodromy map μ taking a potential q∈L2([0,2π]) to , the lift to the universal cover of SL(2,R) of the fundamental matrix map ,
11.
We study some structural aspects of the subspaces of the non-commutative (Haagerup) Lp-spaces associated with a general (non-necessarily semi-finite) von Neumann algebra . If a subspace X of contains uniformly the spaces ?pn, n?1, it contains an almost isometric, almost 1-complemented copy of ?p. If X contains uniformly the finite dimensional Schatten classes Spn, it contains their ?p-direct sum too. We obtain a version of the classical Kadec-Pe?czyński dichotomy theorem for Lp-spaces, p?2. We also give operator space versions of these results. The proofs are based on previous structural results on the ultrapowers of , together with a careful analysis of the elements of an ultrapower which are disjoint from the subspace . These techniques permit to recover a recent result of N. Randrianantoanina concerning a subsequence splitting lemma for the general non-commutative Lp spaces. Various notions of p-equiintegrability are studied (one of which is equivalent to Randrianantoanina's one) and some results obtained by Haagerup, Rosenthal and Sukochev for Lp-spaces based on finite von Neumann algebras concerning subspaces of containing ?p are extended to the general case. 相似文献
12.
Françoise Lust-Piquard 《Advances in Mathematics》2004,185(2):289-327
Let G be a lca group with a fixed g0∈G, spanning an infinite subgroup. Let τj, acting on L2(Gn), be translation by go in the jth coordinate; the discrete derivatives ∂j=I−τj define a discrete Laplacian and discrete Riesz transforms . We get dimension-free estimates
13.
We prove that a first-order linear differential operator G with unbounded operator coefficients is Fredholm on spaces of functions on with values in a reflexive Banach space if and only if the corresponding strongly continuous evolution family has exponential dichotomies on both and and a pair of the ranges of the dichotomy projections is Fredholm, and that the Fredholm index of G is equal to the Fredholm index of the pair. The operator G is the generator of the evolution semigroup associated with the evolution family. In the case when the evolution family is the propagator of a well-posed differential equation u′(t)=A(t)u(t) with, generally, unbounded operators , the operator G is a closure of the operator . Thus, this paper provides a complete infinite-dimensional generalization of well-known finite-dimensional results by Palmer, and by Ben-Artzi and Gohberg. 相似文献
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Let be a simple Lie algebra, and let Mλ be the Verma module over with highest weight λ. For a finite-dimensional -module U we introduce a notion of a regularizing operator, acting in U, which makes the meromorphic family of intertwining operators holomorphic, and conjugates the dynamical Weyl group operators Aw(λ)∈End(U) to constant operators. We establish fundamental properties of regularizing operators, including uniqueness, and prove the existence of a regularizing operator in the case . 相似文献
16.
Let G(p,n) and G(q,n) be the affine Grassmann manifolds of p- and q-planes in Rn, respectively, and let be the Radon transform from smooth functions on G(p,n) to smooth functions on G(q,n) arising from the inclusion incidence relation. When p<q and dimG(p,n)=dimG(p,n), we present a range characterization theorem for via moment conditions. We then use this range result to prove a support theorem for . This complements a previous range characterization theorem for via differential equations when dimG(p,n)<dimG(p,n). We also present a support theorem in this latter case. 相似文献
17.
Daniel Markiewicz 《Journal of Functional Analysis》2003,200(1):237-280
Given a W∗-continuous semigroup φ of unital, normal, completely positive maps of B(H), we introduce its continuous tensor product system . If α is a minimal dilation E0-semigroup of φ with Arveson product system F, then is canonically isomorphic to F. We apply this construction to a class of semigroups of arising from a modified Weyl-Moyal quantization of convolution semigroups of Borel probability measures on . This class includes the heat flow on the CCR algebra studied recently by Arveson. We prove that the minimal dilations of all such semigroups are completely spatial, and additionally, we prove that the minimal dilation of the heat flow is cocyle conjugate to the CAR/CCR flow of index two. 相似文献
18.
Let H be a complex separable Hilbert space and L(H) denote the collection of bounded linear operators on H. An operator A in L(H) is said to be a Cowen-Douglas operator if there exist Ω, a connected open subset of complex plane C, and n, a positive integer, such that
- (a)
- (b)
- for z in Ω;
- (c)
- ; and
- (d)
- for z in Ω.
19.
Let Γ be a finitely generated, torsion-free, two-step nilpotent group. Let C*(Γ) denote the universal C*-algebra of Γ. We show that , where for a unital C*-algebra A, sr(A) is the stable rank of A, and where is the space of one-dimensional representations of Γ. In process, we give a stable rank estimate for maximal full algebras of operator fields over metric spaces. 相似文献