On spectral homomorphisms and continuous functions of Banach algebra elements
Thomas, Gary M. (1979)
Portugaliae mathematica
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Thomas, Gary M. (1979)
Portugaliae mathematica
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Larsen, R. (1971)
Portugaliae mathematica
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Gustavo Corach, Fernando Suárez (1987)
Studia Mathematica
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H. Dales (1982)
Banach Center Publications
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Osamu Hatori, Go Hirasawa, Takeshi Miura (2010)
Open Mathematics
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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 for all a ∈ A, where e is unit element of A. If, in addition, and on M B, then T is an algebra isomorphism. ...
W. Badé, P. Curtis, K. Laursen (1980)
Studia Mathematica
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George Maltese, Regina Wille-Fier (1988)
Studia Mathematica
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V. Müller (1982)
Studia Mathematica
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A. Katavolos, C. Stamatopoulos (1998)
Studia Mathematica
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It is proved that the set Q of quasinilpotent elements in a Banach algebra is an ideal, i.e. equal to the Jacobson radical, if (and only if) the condition [Q,Q] ⊆ Q (or a similar condition concerning anticommutators) holds. In fact, if the inner derivation defined by a quasinilpotent element p maps Q into itself then p ∈ Rad A. Higher commutator conditions of quasinilpotents are also studied. It is shown that if a Banach algebra satisfies such a condition, then every quasinilpotent element...