Displaying similar documents to “On the ideals of extended quasi-nilpotent Banach algebras.”

Alternative noetherian Banach algebras.

M. Benslimane, N. Boudi (1997)

Extracta Mathematicae

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Sinclair and Tullo [6] proved that noetherian Banach algebras are finite-dimensional. In [3], Grabiner studied noetherian Banach modules. In this paper, we are concerned with alternative noetherian Banach algebras. Combining techniques from [3] with techniques and the result from [6], we prove that every alternative noetherian Banach algebra is finite-dimensional.

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]