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- W2079391316 abstract "Let A and B be unital, semisimple commutative Banach algebras with the maximal ideal spaces M A and M B , respectively, and let r(a) be the spectral radius of a. We show that if T: A → B is a surjective mapping, not assumed to be linear, satisfying r(T(a) + T(b)) = r(a + b) for all a; b ∈ A, then there exist a homeomorphism φ: M B → M A and a closed and open subset K of M B such that $$ widehat{Tleft( a right)}left( y right) = left{ begin{gathered} widehat{Tleft( e right)}left( y right)hat aleft( {phi left( y right)} right) y in K hfill widehat{Tleft( e right)}left( y right)overline {hat aleft( {phi left( y right)} right)} y in M_mathcal{B} backslash K hfill end{gathered} right. $$ for all a ∈ A, where e is unit element of A. If, in addition, $$ widehat{Tleft( e right)} = 1 $$ and $$ widehat{Tleft( {ie} right)} = i $$ on M B , then T is an algebra isomorphism." @default.
- W2079391316 created "2016-06-24" @default.
- W2079391316 creator A5020219136 @default.
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- W2079391316 date "2010-05-30" @default.
- W2079391316 modified "2023-09-25" @default.
- W2079391316 title "Additively spectral-radius preserving surjections between unital semisimple commutative Banach algebras" @default.
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- W2079391316 doi "https://doi.org/10.2478/s11533-010-0025-4" @default.
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