Invertibility preserving linear maps on ℒ(𝒳)

Sourour, A.

doi:10.1090/S0002-9947-96-01428-6

Invertibility preserving linear maps on $\mathcal {L}(X)$
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by A. R. Sourour PDF

Trans. Amer. Math. Soc. 348 (1996), 13-30 Request permission

Abstract:

For Banach spaces $X$ and $Y$, we show that every unital bijective invertibility preserving linear map between $\mathcal L(X)$ and $\mathcal L(Y)$ is a Jordan isomorphism. The same conclusion holds for maps between $\mathbb CI+ \mathcal K(X)$ and $\mathbb CI+\mathcal K(Y)$.

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