共查询到20条相似文献,搜索用时 281 毫秒
1.
Kazuyuki Sait 《Journal of Mathematical Analysis and Applications》2009,360(2):369-376
Akemann showed that any von Neumann algebra with a weak* separable dual space has a faithful normal representation on a separable Hilbert space. He posed the question: If a C*-algebra has a weak* separable state space, must it have a faithful representation on a separable Hilbert space? Wright solved this question negatively and showed that a unital C*-algebra has the weak* separable state space if and only if it has a unital completely positive map, into a type I factor on a separable Hilbert space, whose restriction to the self-adjoint part induces an order isomorphism. He called such a C*-algebra almost separably representable. We say that a unital C*-algebra is small if it has a unital complete isometry into a type I factor on a separable Hilbert space. In this paper we show that a unital C*-algebra is small if and only if the state spaces of all n by n matrix algebras over the C*-algebra are weak*-separable. It is natural to ask whether almost separably representable algebras are small or not. We settle this question positively for simple C*-algebras but the general question remains open. 相似文献
2.
We investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras, and give several applications of the surprising fact that certain maps are always weak*-continuous on dual spaces. In particular, if X is a subspace of a C*-algebra A, and if a∈A satisfies aX⊂X, then we show that the function x?ax on X is automatically weak* continuous if either (a) X is a dual operator space, or (b) a*X⊂X and X is a dual Banach space. These results hinge on a generalization to Banach modules of Tomiyama's famous theorem on contractive projections onto a C*-subalgebra. Applications include a new characterization of the σ-weakly closed (possibly nonunital and nonselfadjoint) operator algebras, and a generalization of the theory of W*-modules to the framework of modules over such algebras. We also give a Banach module characterization of σ-weakly closed spaces of operators which are invariant under the action of a von Neumann algebra. 相似文献
3.
We study the K-theory of unital C*-algebras A satisfying the condition that all irreducible representations are finite and of some bounded dimension. We construct
computational tools, but show that K-theory is far from being able to distinguish between various interesting examples. For example, when the algebra A is n-homogeneous, i.e., all irreducible representations are exactly of dimension n, then K*(A) is the topological K-theory of a related compact Hausdorff space, this generalises the classical Gelfand-Naimark theorem, but there are many inequivalent
homogeneous algebras with the same related topological space. For general A we give a spectral sequence computing K*(A) from a sequence of topological K-theories of related spaces. For A generated by two idempotents, this becomes a 6-term long exact sequence. 相似文献
4.
Dmitry Goldstein 《Integral Equations and Operator Theory》1999,33(2):172-174
LetA denote a unital Banach algebra, and letB denote aC
*-algebra which is contained as a unital subalgebra inA. We prove thatB is inverse closed inA if the norms ofA andB coincide. This generalizes well known result about inverse closedness ofC
*-subalgebras inC
*-algebras. 相似文献
5.
Closed Projections and Peak Interpolation for Operator Algebras 总被引:1,自引:0,他引:1
Damon M. Hay 《Integral Equations and Operator Theory》2007,57(4):491-512
The closed one-sided ideals of a C
*-algebra are exactly the closed subspaces supported by the orthogonal complement of a closed projection. Let A be a (not necessarily selfadjoint) subalgebra of a unital C
*-algebra B which contains the unit of B. Here we characterize the right ideals of A with left contractive approximate identity as those subspaces of A supported by the orthogonal complement of a closed projection in B
** which also lies in
. Although this seems quite natural, the proof requires a set of new techniques which may be viewed as a noncommutative version
of the subject of peak interpolation from the theory of function spaces. Thus, the right ideals with left approximate identity
are closely related to a type of peaking phenomena in the algebra. In this direction, we introduce a class of closed projections
which generalizes the notion of a peak set in the theory of uniform algebras to the world of operator algebras and operator
spaces. 相似文献
6.
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
7.
Kaidi El Amin Antonio Morales Campoy Angel Rodríguez Palacios 《manuscripta mathematica》2001,104(4):467-478
We characterize C
*-algebras as those complete normed associative complex algebras having approximate units bounded by one and whose open unit
balls are bounded symmetric domains. Such a characterization follows from the more general fact, also proved in the paper,
that non-commutative JB
*-algebras coincide with complete normed (possibly non-associative) complex algebras having approximate units bounded by one
and whose open unit balls are bounded symmetric domains.
Received: 3 October 2000 / Revised version: 26 January 2001 相似文献
8.
Matthias Neufang 《Journal of Functional Analysis》2005,224(1):217-229
Let A be a Banach algebra, and consider A** equipped with the first Arens product. We establish a general criterion which ensures that A is left strongly Arens irregular, i.e., the first topological centre of A** is reduced to A itself. Using this criterion, we prove that for a very large class of locally compact groups, Ghahramani-Lau's conjecture (cf. [Lau 94] and [Gha-Lau 95]) stating the left strong Arens irregularity of the measure algebra M(G), holds true. (Our methods obviously yield as well the right strong Arens irregularity in the situation considered.)Furthermore, the same condition used above implies that every linear left A**-module homomorphism on A* is automatically bounded and w*-continuous. We finally show that our criterion also yields a partial answer to a question raised by Lau-Ülger (Trans. Amer. Math. Soc. 348 (3) (1996) 1191) on the topological centre of the algebra (A*⊙A)*, for A having a right approximate identity bounded by 1. 相似文献
9.
We prove several versions of Grothendieck’s Theorem for completely bounded linear maps T:E→F
*, when E and F are operator spaces. We prove that if E, F are C
*-algebras, of which at least one is exact, then every completely bounded T:E→F
* can be factorized through the direct sum of the row and column Hilbert operator spaces. Equivalently T can be decomposed as T=T
r
+T
c
where T
r
(resp. T
c
) factors completely boundedly through a row (resp. column) Hilbert operator space. This settles positively (at least partially)
some earlier conjectures of Effros-Ruan and Blecher on the factorization of completely bounded bilinear forms on C
*-algebras. Moreover, our result holds more generally for any pair E, F of “exact” operator spaces. This yields a characterization of the completely bounded maps from a C
*-algebra (or from an exact operator space) to the operator Hilbert space OH. As a corollary we prove that, up to a complete
isomorphism, the row and column Hilbert operator spaces and their direct sums are the only operator spaces E such that both E and its dual E
* are exact. We also characterize the Schur multipliers which are completely bounded from the space of compact operators to
the trace class.
Oblatum 31-I-2002 & 3-IV-2002?Published online: 17 June 2002 相似文献
10.
Subhash J Bhatt 《Proceedings Mathematical Sciences》1985,94(2-3):71-91
Consideration of quotient-bounded elements in a locally convexGB *-algebra leads to the study of properGB *-algebras viz those that admit nontrivial quotient-bounded elements. The construction and structure of such algebras are discussed. A representation theorem for a properGB *-algebra representing it as an algebra of unbounded Hilbert space operators is obtained in a form that unifies the well-known Gelfand-Naimark representation theorem forC *-algebra and two other representation theorems forb *-algebras (also calledlmc *-algebras), one representinga b *-algebra as an algebra of quotient bounded operators and the other as a weakly unbounded operator algebra. A number of examples are discussed to illustrate quotient-bounded operators. An algebra of unbounded operators constructed out of noncommutativeL p-spaces on a regular probability gauge space and the convolution algebra of periodic distributions are analyzed in detail; whereas unbounded Hilbert algebras andL w-integral of a measurable field ofC *-algebras are discussed briefly. 相似文献
11.
In this paper, we construct representatives for all equivalence classes of the unital essential extension algebras of Cuntz algebra by the C*-algebras of compact operators on a separable infinite-dimensional Hilbert space. We also compute their K-groups and semigroups and classify these extension algebras up to isomorphism by their semigroups. 相似文献
12.
Dragan S. Djordjevi 《Journal of Computational and Applied Mathematics》2007,200(2):701-704
In this paper we find the explicit solution of the equation
A*X+X*A=B