منابع مشابه
Invertibility-preserving Maps of C∗-algebras with Real Rank Zero
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...
متن کاملSeparative Exchange Rings and C * - Algebras with Real Rank Zero
For any (unital) exchange ring R whose finitely generated projective modules satisfy the separative cancellation property (A ⊕ A ∼= A ⊕ B ∼= B ⊕ B =⇒ A ∼= B), it is shown that all invertible square matrices over R can be diagonalized by elementary row and column operations. Consequently, the natural homomorphism GL1(R) → K1(R) is surjective. In combination with a result of Huaxin Lin, it follow...
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For a row finite directed graph E, Kumjian, Pask, and Rae-burn proved that there exists a universal C *-algebra C * (E) generated by a Cuntz-Krieger E-family. In this paper we consider two density problems of invertible elements in graph C *-algebras C * (E), and it is proved that C * (E) has stable rank one, that is, the set of all invertible elements is dense in C * (E) (or in its unitization...
متن کاملHigher Rank Graph C∗-algebras
Building on recent work of Robertson and Steger, we associate a C∗–algebra to a combinatorial object which may be thought of as a higher rank graph. This C∗–algebra is shown to be isomorphic to that of the associated path groupoid. Various results in this paper give sufficient conditions on the higher rank graph for the associated C∗–algebra to be: simple, purely infinite and AF. Results concer...
متن کاملExtremal 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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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2002
ISSN: 0022-1236
DOI: 10.1006/jfan.2001.3830