Invertibility-preserving maps of $C^*$-algebras with real rank zero
Kovacs, Istvan
Abstr. Appl. Anal., Tome 2005 (2005) no. 2, p. 685-689 / Harvested from Project Euclid
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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 $\Phi: A\rightarrow B$ is a linear map onto $B$ that preserves the spectrum of elements, then $\Phi$ is a Jordan isomorphism if either $A$ or $B$ is a $C^*$ -algebra of real rank zero. We also generalize a theorem of Russo.
Publié le : 2005-08-22
Classification:  
@article{1128345946,
     author = {Kovacs, Istvan},
     title = {Invertibility-preserving maps of $C^*$-algebras with real rank zero},
     journal = {Abstr. Appl. Anal.},
     volume = {2005},
     number = {2},
     year = {2005},
     pages = { 685-689},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1128345946}
}

Kovacs, Istvan. Invertibility-preserving maps of $C^*$-algebras with real rank zero. Abstr. Appl. Anal., Tome 2005 (2005) no. 2, pp.  685-689. http://gdmltest.u-ga.fr/item/1128345946/