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Linear Maps on C*-Algebras Preserving the Set of Operators that are Invertible in

  • Sang Og Kim (a1) and Choonkil Park (a2)

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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References

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Linear Maps on C*-Algebras Preserving the Set of Operators that are Invertible in

  • Sang Og Kim (a1) and Choonkil Park (a2)

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