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22 August 2005 Invertibility-preserving maps of $C^*$-algebras with real rank zero
Istvan Kovacs
Abstr. Appl. Anal. 2005(6): 685-689 (22 August 2005). DOI: 10.1155/AAA.2005.685


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:AB 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.


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Istvan Kovacs. "Invertibility-preserving maps of $C^*$-algebras with real rank zero." Abstr. Appl. Anal. 2005 (6) 685 - 689, 22 August 2005.


Published: 22 August 2005
First available in Project Euclid: 3 October 2005

zbMATH: 1105.46036
MathSciNet: MR2202956
Digital Object Identifier: 10.1155/AAA.2005.685

Rights: Copyright © 2005 Hindawi

Vol.2005 • No. 6 • 22 August 2005
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