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...
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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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Let A be a C∗-algebra. Let E and F be Hilbert A-modules with E being full. Suppose that θ : E → F is a linear map preserving orthogonality, i.e., 〈θ(x), θ(y)〉 = 0 whenever 〈x, y〉 = 0. We show in this article that if, in addition, A has real rank zero, and θ is an A-module map (not assumed to be bounded), then there exists a central positive multiplier u ∈M(A) such that 〈θ(x), θ(y)〉 = u〈x, y〉 (x...
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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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It is known that the classical Hilbert–Schmidt theorem can be generalized to the case of compact operators in Hilbert A-modules H∗ A over a W ∗-algebra of finite type, i.e. compact operators in H∗ A under slight restrictions can be diagonalized over A. We show that if B is a weakly dense C∗-subalgebra of real rank zero in A with some additional property then the natural extension of a compact o...
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ژورنال
عنوان ژورنال: Infinite Dimensional Analysis, Quantum Probability and Related Topics
سال: 2000
ISSN: 0219-0257,1793-6306
DOI: 10.1142/s0219025700000248