Additively spectral-radius preserving surjections between unital semisimple commutative Banach algebras
Osamu Hatori ; Go Hirasawa ; Takeshi Miura
Open Mathematics, Tome 8 (2010), p. 597-601 / Harvested from The Polish Digital Mathematics Library
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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 Ta^y=Te^ya^φyy∈KTe^ya^φy¯y∈Mℬ∖K for all a ∈ A, where e is unit element of A. If, in addition, Te^=1 and Tie^=i on M B, then T is an algebra isomorphism.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:269004 
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     author = {Osamu Hatori and Go Hirasawa and Takeshi Miura},
     title = {Additively spectral-radius preserving surjections between unital semisimple commutative Banach algebras},
     journal = {Open Mathematics},
     volume = {8},
     year = {2010},
     pages = {597-601},
     zbl = {1211.46052},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0025-4}
}

Osamu Hatori; Go Hirasawa; Takeshi Miura. Additively spectral-radius preserving surjections between unital semisimple commutative Banach algebras. Open Mathematics, Tome 8 (2010) pp. 597-601. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0025-4/

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