Invertibility-preserving maps of C ∗ -algebras with real rank zero

Istvan Kovacs

Abstract and Applied Analysis, 2005, vol. 2005, 1-5

Abstract:

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 and Φ : A → B is a linear map onto B that preserves the spectrum of elements, then Φ is a Jordan isomorphism if either A or B is a C ∗ -algebra of real rank zero. We also generalize a theorem of Russo.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:356539

DOI: 10.1155/AAA.2005.685

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