Geodesic
Linear Maps on C*-Algebras Preserving the Set of Operators that are Invertible in
Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 141-146

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DOI

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.
DOI : 10.4153/CMB-2010-087-x
Mots-clés : 47B48, 47A10, 46H10, preservers, Jordan automorphisms, invertible operators, zero products 
Kim, Sang Og; Park, Choonkil. Linear Maps on C*-Algebras Preserving the Set of Operators that are Invertible in. Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 141-146. doi: 10.4153/CMB-2010-087-x
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     year = {2011},
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