Entire functions in Bo-algebras
B. Mitiagin, S. Rolewicz, W. Żelazko (1962)
Studia Mathematica
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B. Mitiagin, S. Rolewicz, W. Żelazko (1962)
Studia Mathematica
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Abdellah El Kinani (2000)
Revista Matemática Complutense
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We obtain that the power maps are equicontinuous at zero in any Baire locally convex algebra with a continuous product in which all entire functions operate; whence is m-convex in the commutative case. As a consequence, we get the same result of Mityagin, Rolewicz and Zelazko for commutative B-algebras.
Chilana, Ajit Kaur, Kaushik, Vimla (1979)
Portugaliae mathematica
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Mohamed Oudadess (1990)
Publicacions Matemàtiques
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Entire functions operate in complete locally A-convex algebras but not continuously. Actually squaring is not always continuous. The counterexample we give is multiplier algebra.
El Kinani, A., Oudadess, M. (1997)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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V. Müller (1991)
Studia Mathematica
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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.
Joaquim Bruna (1981)
Studia Mathematica
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S. Rolewicz (1963)
Studia Mathematica
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W. Żelazko (1996)
Studia Mathematica
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We construct two examples of complete multiplicatively convex algebras with the property that all their maximal commutative subalgebras and consequently all commutative closed subalgebras are Banach algebras. One of them is non-metrizable and the other is metrizable and non-Banach. This solves Problems 12-16 and 22-24 of [7].
Günter Czichowski (1983)
Studia Mathematica
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