A characterization of maximal ideals in commutative Banach algebras
J. Kahane, W. Żelazko (1968)
Studia Mathematica
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J. Kahane, W. Żelazko (1968)
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Krzysztof Jarosz (1996)
Studia Mathematica
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Let A be a complex Banach algebra with a unit e, let T, φ be continuous functionals, where T is linear, and let F be a nonlinear entire function. If T ∘ F = F ∘ φ and T(e) = 1 then T is multiplicative.
George Maltese, Regina Wille-Fier (1988)
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Gerd Herzog, Christoph Schmoeger (2004)
Studia Mathematica
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Let 𝒜 be a Banach algebra over ℂ with unit 1 and 𝑓: ℂ → ℂ an entire function. Let 𝐟: 𝒜 → 𝒜 be defined by 𝐟(a) = 𝑓(a) (a ∈ 𝒜), where 𝑓(a) is given by the usual analytic calculus. The connections between the periods of 𝑓 and the periods of 𝐟 are settled by a theorem of E. Vesentini. We give a new proof of this theorem and investigate further properties of periods of 𝐟, for example in C*-algebras.
Marc P. Thomas (2009)
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It is a famous conjecture that every derivation on each Banach algebra leaves every primitive ideal of the algebra invariant. This conjecture is known to be true if, in addition, the derivation is assumed to be continuous. It is also known to be true if the algebra is commutative, in which case the derivation necessarily maps into the (Jacobson) radical. Because I. M. Singer and J. Wermer originally raised the question in 1955 for the case of commutative Banach algebras, the conjecture...
Krzysztof Jarosz (1997)
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Let A be a complex Banach algebra with a unit e, let F be a nonconstant entire function, and let T be a linear functional with T(e)=1 and such that T∘F: A → ℂ is nonsurjective. Then T is multiplicative.
Volker Runde (1993)
Studia Mathematica
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Let A be a Banach algebra, and let D : A → A be a (possibly unbounded) derivation. We are interested in two problems concerning the range of D: 1. When does D map into the (Jacobson) radical of A? 2. If [a,Da] = 0 for some a ∈ A, is Da necessarily quasinilpotent? We prove that derivations satisfying certain polynomial identities map into the radical. As an application, we show that if [a,[a,[a,Da]]] lies in the prime radical of A for all a ∈ A, then D maps into the radical. This generalizes...
Graham Allan, Allan Sinclair (1976)
Studia Mathematica
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W. Żelazko (1968)
Studia Mathematica
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W. Żelazko (1969)
Colloquium Mathematicae
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Niels Gronbaek (1982)
Mathematica Scandinavica
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Joel F. Feinstein, Herbert Kamowitz (2010)
Banach Center Publications
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This paper is a continuation of our study of compact, power compact, Riesz, and quasicompact endomorphisms of commutative Banach algebras. Previously it has been shown that if B is a unital commutative semisimple Banach algebra with connected character space, and T is a unital endomorphism of B, then T is quasicompact if and only if the operators Tⁿ converge in operator norm to a rank-one unital endomorphism of B. In this note the discussion is extended in two ways: we discuss endomorphisms...
Konin Koua (1985)
Mathematica Scandinavica
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El Harti, R. (2004)
International Journal of Mathematics and Mathematical Sciences
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S. Levi (1982)
Banach Center Publications
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