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Displaying similar documents to “Commutative, radical amenable Banach algebras”

Some results about Beurling algebras with applications to operator theory

Thomas Vils Pedersen (1995)

Studia Mathematica

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We prove that certain maximal ideals in Beurling algebras on the unit disc have approximate identities, and show the existence of functions with certain properties in these maximal ideals. We then use these results to prove that if T is a bounded operator on a Banach space X satisfying ∥ T n ∥ = O ( n β ) as n → ∞ for some β ≥ 0, then ∑ n = 1 ∞ ∥ ( 1 - T ) n x ∥ / ∥ ( 1 - T ) n - 1 x ∥ diverges for every x ∈ X such that ( 1 - T ) [ β ] + 1 x ≠ 0 .

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]