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- W2139992504 abstract "Let $A$ be a semisimple Banach algebra, and let $Omega _A$ be its spectral unit ball. We show that every holomorphic map $Gcolon Omega _Ato Omega _A$ satisfying $G(0)=0$ and $Gâ(0)=I$ fixes those elements of $Omega _A$ which belong to the centre of $A$, but not necessarily any others. Using this, we deduce that the automorphisms of $Omega _A$ all leave the centre invariant. As a further application, we give a new proof of Nagasawaâs generalization of the Banach-Stone theorem." @default.
- W2139992504 created "2016-06-24" @default.
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- W2139992504 date "1996-01-01" @default.
- W2139992504 modified "2023-09-23" @default.
- W2139992504 title "A Cartan theorem for Banach algebras" @default.
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- W2139992504 doi "https://doi.org/10.1090/s0002-9939-96-03197-8" @default.
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