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Generalizations of spectrally multiplicative surjections between uniform algebras. (English) Zbl 1209.46027

Let \(A\) be a Banach algebra. A map \(S:A\to A\) satisfies the spectrally multiplicative condition if \(\sigma(S(x)S(y))=\sigma(xy)\) for all \(x,y\) in \(A\). A result due to Molnár says that if a surjection \(S:C(X)\to C(X)\) is spectrally multiplicative, then it is an isometric algebra automorphisms. Adding to already existing ones, the authors obtain several further generalizations of this result. They are too technical to be shortly described, but they are of interest to a specialist in the field.

MSC:

46J10 Banach algebras of continuous functions, function algebras
46J20 Ideals, maximal ideals, boundaries
47A10 Spectrum, resolvent
47B48 Linear operators on Banach algebras
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