共查询到20条相似文献,搜索用时 46 毫秒
1.
Let n
i
,m
j
> 1. In [5], the sperical noncommutative torus
was defined by twisting
in
by a totally skew multiplier p on
for T
pd
a pd-homogeneous C*-algebra over
. It is shown that
is strongly Morita equivalent to
.
This work is supported by Grant No. 1999-2-102-001-3 from the interdisciplinary research program year of the KOSEF 相似文献
2.
3.
T. V. Shul’man 《Mathematical Notes》2005,77(5-6):726-734
The results of Kasparov, Connes, Higson, and Loring imply the coincidence of the functors [[qℂ ⊗ K, B ⊗ K]] = [[C
0(ℝ2) ⊗ K, B ⊗ K]] for any C*-algebra B; here[[A, B]] denotes the set of homotopy classes of asymptotic homomorphisms from A to B. Inthe paper, this assertion is strengthened; namely, it is shown that the algebras qℂ ⊗ K and C
0(ℝ2) ⊗ K are equivalent in the category whose objects are C*-algebras and morphisms are classes of homotopic asymptotic homomorphisms. Some geometric properties of the obtained equivalence are studied. Namely, the algebras qℂ ⊗ K and C
0(ℝ2) ⊗ K are represented as fields of C*-algebras; it is proved that the equivalence is not fiber-preserving, i.e., is does not take fibers to fibers. It is also proved that the algebras under consideration are not homotopy equivalent.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 788–796.Original Russian Text Copyright ©2005 by T. V. Shul’man. 相似文献
4.
S. J. Bhatt 《Proceedings Mathematical Sciences》2001,111(1):65-94
UniversalC*-algebrasC*(A) exist for certain topological *-algebras called algebras with aC*-enveloping algebra. A Frechet *-algebraA has aC*-enveloping algebra if and only if every operator representation ofA mapsA into bounded operators. This is proved by showing that every unbounded operator representation π, continuous in the uniform
topology, of a topological *-algebraA, which is an inverse limit of Banach *-algebras, is a direct sum of bounded operator representations, thereby factoring through
the enveloping pro-C*-algebraE(A) ofA. Given aC*-dynamical system (G,A,α), any topological *-algebraB containingC
c
(G,A) as a dense *-subalgebra and contained in the crossed productC*-algebraC*(G,A,α) satisfiesE(B) =C*(G,A,α). IfG = ℝ, ifB is an α-invariant dense Frechet *-subalgebra ofA such thatE(B) =A, and if the action α onB ism-tempered, smooth and by continuous *-automorphisms: then the smooth Schwartz crossed productS(ℝ,B,α) satisfiesE(S(ℝ,B,α)) =C*(ℝ,A,α). WhenG is a Lie group, theC
∞-elementsC
∞(A), the analytic elementsC
ω(A) as well as the entire analytic elementsC
є(A) carry natural topologies making them algebras with aC*-enveloping algebra. Given a non-unitalC*-algebraA, an inductive system of idealsI
α is constructed satisfyingA =C*-ind limI
α; and the locally convex inductive limit ind limI
α is anm-convex algebra with theC*-enveloping algebraA and containing the Pedersen idealK
a
ofA. Given generatorsG with weakly Banach admissible relationsR, we construct universal topological *-algebraA(G, R) and show that it has aC*-enveloping algebra if and only if (G, R) isC*-admissible. 相似文献
5.
Lining Jiang 《Siberian Mathematical Journal》2009,50(2):360-367
Let be a C*-discrete quantum group and let be the discrete quantum group associated with . Suppose that there exists a continuous action of on a unital C*-algebra so that becomes a -algebra. If there is a faithful irreducible vacuum representation π of on a Hilbert space H = with a vacuum vector Ω, which gives rise to a -invariant state, then there is a unique C*-representation (θ, H) of supplemented by the action. The fixed point subspace of under the action of is exactly the commutant of θ().
相似文献
6.
A generalization is given of the canonical map from a discrete group into K
1 of the group C
*-algebra. Our map also generalizes Rieffel's construction of a projection in an irrational rotation C
*-algebra. 相似文献
7.
Choonkil PARK Jian Lian CUI 《数学学报(英文版)》2007,23(11):1919-1936
Let X and Y be vector spaces. The authors show that a mapping f : X →Y satisfies the functional equation 2d f(∑^2d j=1(-1)^j+1xj/2d)=∑^2dj=1(-1)^j+1f(xj) with f(0) = 0 if and only if the mapping f : X→ Y is Cauchy additive, and prove the stability of the functional equation (≠) in Banach modules over a unital C^*-algebra, and in Poisson Banach modules over a unital Poisson C*-algebra. Let A and B be unital C^*-algebras, Poisson C^*-algebras or Poisson JC^*- algebras. As an application, the authors show that every almost homomorphism h : A →B of A into is a homomorphism when h((2d-1)^nuy) =- h((2d-1)^nu)h(y) or h((2d-1)^nuoy) = h((2d-1)^nu)oh(y) for all unitaries u ∈A, all y ∈ A, n = 0, 1, 2,....
Moreover, the authors prove the stability of homomorphisms in C^*-algebras, Poisson C^*-algebras or Poisson JC^*-algebras. 相似文献
8.
Cheng Jun Hou 《数学学报(英文版)》2008,24(6):983-996
We introduce two notions of the pressure in operator algebras, one is the pressure Pα(π, T) for an automorphism α of a unital exact C^*-algebra A at a self-adjoint element T in A with respect to a faithful unital *-representation π the other is the pressure Pτ,α(T) for an automorphism α of a hyperfinite von Neumann algebra M at a self-adjoint element T in M with respect to a faithful normal α-invariant state τ. We give some properties of the pressure, show that it is a conjugate invaxiant, and also prove that the pressure of the implementing inner automorphism of a crossed product A×α Z at a self-adjoint operator T in A equals that of α at T. 相似文献
9.
Assume that each completely irrational noncommutative torus is realized as an inductive limit of circle algebras, and that for a completely irrational noncommutative torus Aw of rank m there are a completely irrational noncommutative torus Aρ of rank m and a positive integer d such that tr(Aw)=1/d.tr(Aρ).It is proved that the set of all C^*-algebras of sections of locally trivial C^*-algebra bundles over S^2 with fibres Aω has a group sturcture,denoted by π1^s(Aut(Aω)),which is isomorphic to Zif Ed>1 and {0} if d>1.Let Bcd be a cd-homogeneous C^*-algebra over S^2×T^2 of which no non-trivial matrix algebra can be factored out.The spherical noncommutative torus Sρ^cd is defined by twisting C^*(T2×Z^m-2) in Bcd ×C^*(Z^m-3) by a totally skew multiplier ρ on T^2×Z^m-2。It is shown that Sρ^cd×Mρ∞ is isomorphic to C(S^2)×C^*(T^2×Z^m-2,ρ)× Mcd(C)×Mρ∞ if and only if the set of prime factors of cd is a subset of the set of prime factors of p. 相似文献
10.
We study the weak law of large numbers and the central limit theorem for non-commutative random variables. We first define the concepts of variance and expectation for probability measures on homogeneous spaces, and formulate the weak law of large numbers and the central limit theorem for probability measures on locally compact groups. Then, we consider the non-commutative case, where the homogeneous space is replaced by a C*-algebra
that is equipped with a locally compact group G of automorphisms. We define the concepts of variance and expectation in the non-commutative situation. Furthermore, we prove that the weak law of large numbers and the central limit theorem hold for non-commutative random variables on
if they hold on the group G of automorphisms. 相似文献
11.
Bernhard Burgstaller 《Monatshefte für Mathematik》2009,157(1):1-11
There exists a separable exact C*-algebra A which contains all separable exact C*-algebras as subalgebras, and for each norm-dense measure μ on A and independent μ-distributed random elements x
1, x
2, ... we have . Further, there exists a norm-dense non-atomic probability measure μ on the Cuntz algebra such that for an independent sequence x
1, x
2, ... of μ-distributed random elements x
i
we have . We introduce the notion of the stochastic rank for a unital C*-algebra and prove that the stochastic rank of C([0, 1]
d
) is d.
B. Burgstaller was supported by the Austrian Schr?dinger stipend J2471-N12. 相似文献
12.
Chun-Gil Park Hahng-Yun Chu Won-Gil Park Hee-Jeong Wee 《Czechoslovak Mathematical Journal》2005,55(4):1055-1065
It is shown that every almost linear Pexider mappings f, g, h from a unital C*-algebra
into a unital C*-algebra ℬ are homomorphisms when f(2
n
uy) = f(2
n
u)f(y), g(2
n
uy) = g(2
n
u)g(y) and h(2
n
uy) = h(2
n
u)h(y) hold for all unitaries u ∈
, all y ∈
, and all n ∈ ℤ, and that every almost linear continuous Pexider mappings f, g, h from a unital C*-algebra
of real rank zero into a unital C*-algebra ℬ are homomorphisms when f(2
n
uy) = f(2
n
u)f(y), g(2
n
uy) = g(2
n
u)g(y) and h(2
n
uy) = h(2
n
u)h(y) hold for all u ∈ {v ∈
: v = v* and v is invertible}, all y ∈
and all n ∈ ℤ.
Furthermore, we prove the Cauchy-Rassias stability of *-homomorphisms between unital C*-algebras, and ℂ-linear *-derivations on unital C*-algebras.
This work was supported by Korea Research Foundation Grant KRF-2003-042-C00008.
The second author was supported by the Brain Korea 21 Project in 2005. 相似文献
13.
Subhash J. Bhatt 《Proceedings Mathematical Sciences》2006,116(2):161-173
Given anm-tempered strongly continuous action α of ℝ by continuous*-automorphisms of a Frechet*-algebraA, it is shown that the enveloping ↡-C
*-algebraE(S(ℝ, A∞, α)) of the smooth Schwartz crossed productS(ℝ,A
∞, α) of the Frechet algebra A∞ of C∞-elements ofA is isomorphic to the Σ-C
*-crossed productC
*(ℝ,E(A), α) of the enveloping Σ-C
*-algebraE(A) ofA by the induced action. WhenA is a hermitianQ-algebra, one getsK-theory isomorphismRK
*(S(ℝ, A∞, α)) =K
*(C
*(ℝ,E(A), α) for the representableK-theory of Frechet algebras. An application to the differential structure of aC
*-algebra defined by densely defined differential seminorms is given. 相似文献
14.
Jeffrey L. BOERSEMA 《数学学报(英文版)》2007,23(10):1827-1832
We prove analogs of the Kaplansky Density Theorem and the Kadison Transitivity Theorem for irreducible representations of a real C*-algebra on a real Hilbert space. Specifically, if a C*-algebra is acting irreducibly on a real Hilbert space, then the Hilbert space has either a real, complex, or quaternionic structure with respect to which the density and transitivity theorems hold. 相似文献
15.
Abdellah El Kinani 《Rendiconti del Circolo Matematico di Palermo》2008,57(2):229-238
We endow any proper A-convex H*-algebra (E, τ) with a locally pre-C*-topology. The latter is equivalent to that introduced by the pre C*-norm given by Ptàk function when (E, τ) is a Q-algebra. We also prove that the algebra of complex numbers is the unique proper locally A-convex H*-algebra which is barrelled and Q-algebra.
相似文献
16.
17.
The structure of the groupoidG associated with the ToeplitzC
*-algebraC
*(Ω) of the L-shaped domain is discussed. The detailed characterization ofM
∞ by the classification of the closed subgroup of the Euclidean space is presented.
Project supported partially by the National Natural Science Foundation of China, Fok Yingtung Educational Foundation and the
Foundation of the State Education Commission of China. 相似文献
18.
Sh. A. Ayupov 《Functional Analysis and Its Applications》2004,38(4):302-304
Let R be a real AW
*-algebra, and suppose that its complexification M = R + iR is also a (complex) AW
*-algebra. We prove that R is of type I if and only if so is M.Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 38, No. 4, pp. 79–81, 2004Original Russian Text Copyright © by Sh. A. Ayupov 相似文献
19.
Choonkil Park 《Acta Appl Math》2008,102(1):71-85
This paper is a survey on the Hyers–Ulam–Rassias stability of the following Cauchy–Jensen functional equation in C
*-algebras:
The concept of Hyers–Ulam–Rassias stability originated from the Th.M. Rassias’ stability theorem (Rassias in Proc. Am. Math.
Soc. 72:297–300, [1978]).
This work was supported by the research fund of Hanyang University (HY-2007-S). 相似文献
20.