Abstract
In 1996, Harris and Kadison posed the following problem: show that a linear bijection between -algebras that preserves the identity and the set of invertible elements is a Jordan isomorphism. In this paper, we show that if and are semisimple Banach algebras and is a linear map onto that preserves the spectrum of elements, then is a Jordan isomorphism if either or is a -algebra of real rank zero. We also generalize a theorem of Russo.
Citation
Istvan Kovacs. "Invertibility-preserving maps of $C^*$-algebras with real rank zero." Abstr. Appl. Anal. 2005 (6) 685 - 689, 22 August 2005. https://doi.org/10.1155/AAA.2005.685
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