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ISSN 1088-6850(e) ISSN 0002-9947(p)

Invertibility preserving linear maps on $\mathcal L(X)$

Author(s): A. R. Sourour
Journal: Trans. Amer. Math. Soc. 348 (1996), 13-30.
MSC (1991): Primary 47B48, 47B49; Secondary 47A10
MathSciNet review: 1311919
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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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