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

Istvan Kovacs

Abstract and Applied Analysis, 2005, vol. 2005, issue 6, 685-689

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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https://doi.org/10.1155/AAA.2005.685

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2005:y:2005:i:6:p:685-689

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