منابع مشابه
Extremal Richness of Multiplier and Corona Algebras of Simple C∗-algebras with Real Rank Zero
In this paper we investigate the extremal richness of the multiplier algebra M(A) and the corona algebra M(A)/A, for a simple C∗-algebra A with real rank zero and stable rank one. We show that the space of extremal quasitraces and the scale of A contain enough information to determine whether M(A)/A is extremally rich. In detail, if the scale is finite, then M(A)/A is extremally rich. In import...
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A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely the class of simple C*-algebras which are inductive limits of continuous-trace C*-algebras whose building blocks have their spectrum homeomorphic to the interval [0, 1] or to a finite disjoint union of closed intervals. In particular, a classification of those stably AI algebras which ar...
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Let X be a second countable, path connected, compact metric space and let A be a unital separable simple exact Z-stable real rank zero C∗-algebra. We classify all the embeddings (up to approximate unitary equivalence) of C(X) into A. Specifically, we prove the following: Theorem: Let α ∈ KL(C(X), A)+,1 and let λ : T (A) → T (C(X)) be an affine continuous map such that (i) if h ∈ Aff(T (C(X))) i...
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In 1996, Harris and Kadison posed the following problem: show that a linear bijection between C∗-algebras that preserves the identity and the set of invertible elements is a Jordan isomorphism. In this paper, we show that if A and B are semisimple Banach algebras andΦ : A→ B is a linear map onto B that preserves the spectrum of elements, thenΦ is a Jordan isomorphism if either A or B is a C∗-al...
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We show that, if A is a separable simple unital C-algebra which absorbs the Jiang–Su algebra Z tensorially and which has real rank zero and finite decomposition rank, then A is tracially AF in the sense of Lin, without any restriction on the tracial state space. As a consequence, the Elliott conjecture is true for the class of C-algebras as above which, additionally, satisfy the Universal Coeff...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2003
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-03-06995-8