共查询到20条相似文献,搜索用时 31 毫秒
1.
Sun Huarong 《数学年刊B辑(英文版)》1992,13(4):463-470
This paper discusses the ideal structure in tensor product $A\bigotimes B$ of C^*-algebra A and B,and introduces the concept of property (I) and property (K) with respect to the problem.When A is an AF(or scattered) C^*-algebra,it is shown that for any C^*-algebra B,the ideals in $A\bigotimes B$ can be expressed by those of A and B. 相似文献
2.
A Banach partial *-algebra is a locally convex partial *-algebra whose total space is a Banach space. A Banach partial *-algebra is said to be of type (B) if it possesses a generating family of multiplier spaces that are also Banach spaces. We describe the basic properties of such objects and display a number of examples, namely L p -like function spaces and spaces of operators on Hilbert scales. 相似文献
3.
In this paper injective real W*-algebras are investigated. It is shown that injectivity is equivalent to the property of E (extension property). It is proven that a real W*-algebra is injective iff its hermitian part is injective, and it is equivalent to, that the enveloping W*-algebra is also injective. Moreover, it is shown that if the second dual space of a real C*-algebra is injective, then the real C*-algebra is nuclear. 相似文献
4.
George A. Elliott Katsunori Kawamura 《Transactions of the American Mathematical Society》2008,360(9):4841-4862
The category of Hilbert C*-modules over a given C*-algebra is shown to be equivalent to a certain simply described category of Hilbert bundles (i.e., continuous fields of Hilbert spaces) over the space of pure states of the C*-algebra with the zero functional adjoined.
5.
Lin Huaxin 《数学年刊B辑(英文版)》1992,13(4):422-429
Let A be a C~*-algebra and x an element in A. the following invariant subspace problem is considered: Does there exist an irreducible representation π of A such that π(x) has a non-trivial invarint subspace? And a positive solution of the problem for finite separable matroid C~*-algebras is given. Also the eigenvalues Of elements in C~*-algebras is considered. Some versions of Fredholm Alternatives are given. 相似文献
6.
N. T. Nemesh 《Functional Analysis and Its Applications》2016,50(2):157-159
A criterion for the topological injectivity of an AW*-algebra as a right Banach module over itself is given. A necessary condition for a C* -algebra to be topologically injective is obtained. 相似文献
7.
8.
本文研究Pontrjagin空间上一般算子代数弱闭和一致闭的等价条件,得到定理:设C0(U),C1(U,L,R,D,V),C2a(U),C2b(U,R),C3a(U),C3b(U,R)分别是Ⅱk空间上第0,Ⅰ,Ⅱa,Ⅱb,Ⅲa和Ⅲb类的算子代数,则(1)C0(U),C2a(U)或C3a(U)为一致闭(弱闭)的等价条件是U是Hibert空间G上的C*-代数(W*-代数;(2)C1(U,L,R,D,V)为一致闭(弱闭)的等价条件是U是Hibert空间H上的C*-代数(W*-代数),并且R是闭子空间,V是闭算子,L对称闭的;(3)C2b(U,R)或C3b(U,R)为一致闭(弱闭)的等价条件是U是Hibert空间H上的C*-代数(W*-代数),并且R是闭子空间. 相似文献
9.
Michael Frank 《Mathematische Nachrichten》1995,175(1):61-83
The aim of the present paper is to describe self-duality and C*-reflexivity of Hilbert A-modules ?? over monotone complete C*-algebras A by the completeness of the unit ball of ?? with respect to two types of convergence being defined, and by a structural criterion. The derived results generalize earlier results ofH. Widom [Duke Math. J. 23, 309-324, MR 17 # 1228] and W. L. Paschke [Trans. Amer. Mat. Soc. 182 , 443-468, MR 50 # 8087, Canadian J. Math. 26, 1272-1280, MR 57 # 10433]. For Hilbert C*-modules over commutative AW*-algebras the equivalence of the self-duality property and of the Kaplansky-Hilbert property is reproved, (cf. M. Ozawa [J. Math. Soc. Japan 36, 589-609, MR 85 # 46068]). Especially, one derives that for a C*-algebra A the A-valued inner product of every Hilbert A-module ?? can be continued to an A-valued inner product on it's A-dual Banach A-module ??' turning ??' to a self-dual Hilbert A-module if and only if A is monotone complete (or, equivalently, additively complete) generalizing a result of M. Hamana [Internat. J. Math. 3 (1992), 185 - 204]. A classification of countably generated self-dual Hilbert A-modules over monotone complete C*-algebras A is established. The set of all bounded module operators End ′(??) on self-dual Hilbert A-modules ?? over monotone complete C*-algebras A is proved again to be a monotone complete C*-algebra. Applying these results a Weyl-Berg type theorem is proved. 相似文献
10.
We study the complexification of real Hilbert -modules over real -algebras. We give an example of a Hilbert -module that is not the complexification of any Hilbert -module, where is a real -algebra.
11.
We prove that an adjointable contraction acting on a countably generated Hilbert module over a separable unital C*-algebra is compact if and only if the set of its second contractive perturbations is separable.
12.
We develop a Hilbert module version of the Haagerup property for general C*-algebras ${{\mathcal{A} \subseteq \mathcal{B}}}$ . We show that if ${\alpha : \Gamma \curvearrowright \mathcal{A}}$ is an action of a countable discrete group Γ on a unital C*-algebra ${\mathcal{A}}$ , then the reduced C*-algebra crossed product ${\Gamma \ltimes _{\alpha, r} \mathcal{A}}$ has the Hilbert ${\mathcal{A}}$ -module Haagerup property if and only if the action α has the Haagerup property. We are particularly interested in the case when ${\mathcal{A} = C(X)}$ is a unital commutative C*-algebra. We compare the Haagerup property of such an action ${\alpha: \Gamma \curvearrowright C(X)}$ with the two special cases when (1) Γ has the Haagerup property and (2) Γ is coarsely embeddable into a Hilbert space. We also prove a contractive Schur mutiplier characterization for groups coarsely embeddable into a Hilbert space, and a uniformly bounded Schur multiplier characterization for exact groups. 相似文献
13.
Martin Mathieu 《Proceedings of the American Mathematical Society》1998,126(4):1133-1138
A condition on a derivation of an arbitrary C*-algebra is presented entailing that it is implemented as an inner derivation by a local multiplier.
14.
Salvatore Triolo 《印度理论与应用数学杂志》2012,43(6):601-617
Every C*-algebra $\mathfrak{A}$ has a faithful *-representation π in a Hilbert space $\mathcal{H}$ . Consequently it is natural to pose the following question: under which conditions, the completion of a C*-algebra in a weaker than the given one topology, can be realized as a quasi *-algebra of operators? The present paper presents the possibility of extending the well known Gelfand — Naimark representation of C*-algebras to certain Banach C*-modules. 相似文献
15.
In this paper we define and study chain conditions for Hilbert C*-modules through their C*-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C*-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C*-algebra with a faithful conditional expectation. 相似文献
16.
Given a C^*-algebra A and a comultiplication Ф on A, we show that the pair (A, Ф) is a compact quantum group if and only if the associated multiplier Hopf ^*-algebra (A, ФA) is a compact Hopf ^*-algebra. 相似文献
17.
We offer some extensions to C*-algebra elements of factorization properties of EP operators on a Hilbert space. 相似文献
18.
A Hilbert C*-module is a generalization of a Hilbert space for which the inner
product takes its values in a C*-algebra instead of the complex numbers. We use the bracket
product to construct some Hilbert C*-modules over a group C*-algebra which is generated by the
group of translations associated with a wavelet. We shall investigate bracket products and their
Fourier transform in the space of square integrable functions in Euclidean space. We will also show
that some wavelets are associated with Hilbert C*-modules over the space of essentially bounded
functions over higher dimensional tori. 相似文献
19.
共变完全多正线性映射的共变投射表示 总被引:1,自引:0,他引:1
研究了C*-代数中的共变完全多正线性映射,证明了共变完全多正线性映射可以诱导Hilbert C*-模上的共变投射表示,并且给出了共变完全多正线性映射的KS- GNS(Kasparov,Stinespring,Gel’fand,Naimark,Segal)构造. 相似文献
20.
Hirokazu Nishimura 《Mathematical Logic Quarterly》1993,39(1):241-250
Just as Kaplansky [4] has introduced the notion of an AW*-module as a generalization of a complex Hilbert space, we introduce the notion of an AL*-algebra, which is a generalization of that of an L*-algebra invented by Schue [9, 10]. By using Boolean valued methods developed by Ozawa [6–8], Takeuti [11–13] and others, we establish its basic properties including a fundamental structure theorem. This paper should be regarded as a continuation or our previous paper [5], the familiarity with which is presupposed. MSC: 03C90, 03E40, 17B65, 46L10. 相似文献