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Keywords:
linear preserver; noninvertible element; semisimple Banach algebra; socle
linear preserver; noninvertible element; semisimple Banach algebra; socle
Summary:
It is proved that a linear surjection $\Phi \:\mathcal A\rightarrow \mathcal B$, which preserves noninvertibility between semisimple, unital, complex Banach algebras, is automatically injective.
References:
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[4] A. R. Sourour: Invertibility preserving maps on $L(X)$. Trans. Amer. Math. Soc. 348 (1996), 13–30. DOI 10.1090/S0002-9947-96-01428-6 | MR 1311919
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