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Linear Maps on C*-Algebras Preserving the Set of Operators that are Invertible in ![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20190730041447828-0117:S0008439500017902:S0008439500017902_inline1.gif?pub-status=live)
Published online by Cambridge University Press: 20 November 2018
Abstract
For ${{C}^{*}}$-algebras
$\mathcal{A}$ of real rank zero, we describe linear maps
$\phi $ on
$\mathcal{A}$ that are surjective up to ideals
$\mathcal{J}$, and
$\text{ }\pi \text{ (}A\text{)}$ is invertible in
$\mathcal{A}/\mathcal{J}$ if and only if
$\text{ }\pi \text{ (}\phi (A))$ is invertible in
$\mathcal{A}/\mathcal{J}$, where
$A\,\in \,\mathcal{A}$ and
$\text{ }\pi \text{ }\text{:}\mathcal{A}\to \mathcal{A}\text{/}\mathcal{J}$ is the quotient map. We also consider similar linear maps preserving zero products on the Calkin algebra.
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- Research Article
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- Copyright © Canadian Mathematical Society 2011