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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Author: 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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Additional Information

A. R. Sourour
Affiliation: Department of Mathematics and Statistics, University of Victoria, Victoria, B.C. V8W 3P4, Canada

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01428-6
PII: S 0002-9947(96)01428-6
Keywords: Invertibility preserving maps, Jordan homomorphism
Received by editor(s): October 26, 1993
Additional Notes: Supported in part by grants from the Natural Sciences and Engineering Research Council (Canada), and from the University of Victoria
Article copyright: © Copyright 1996 American Mathematical Society