Displaying similar documents to “Fréchet algebras and formal power series”

A note on topologically nilpotent Banach algebras

P. Dixon, V. Müller (1992)

Studia Mathematica

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A Banach algebra A is said to be topologically nilpotent if s u p ∥ x ₁ . . . . . . x n ∥ 1 / n : x i ∈ A , ∥ x i ∥ ≤ 1 ( 1 ≤ i ≤ n ) tends to 0 as n → ∞. We continue the study of topologically nilpotent algebras which was started in [2]

Raising bounded groups and splitting of radical extensions of commutative Banach algebras

W. Bade, P. Curtis, A. Sinclair (2000)

Studia Mathematica

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Let A be a commutative unital Banach algebra and let A/ℛ be the quotient algebra of A modulo its radical ℛ. This paper is concerned with raising bounded groups in A/ℛ to bounded groups in the algebra A. The results will be applied to the problem of splitting radical extensions of certain Banach algebras.

Stable inverse-limit sequences, with application to Predict algebras

Graham Allan (1996)

Studia Mathematica

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The notion of a stable inverse-limit sequence is introduced. It provides a sufficient (and, for sequences of abelian groups, necessary) condition for the preservation of exactness by the inverse-limit functor. Examples of stable sequences are provided through the abstract Mittag-Leffler theorem; the results are applied in the theory of Fréchet algebras.