What question did this study set out to answer?

The aim is to characterize n-weak amenability for triangular Banach algebras without assumptions on the algebras involved.

February 25, 2026SHILAP Revista de lepidopterología0 citationsOpen Access

More on Weak Amenability of Triangular Banach Algebras

MAMahdieh Alikahi MRMohammad Ramezanpour

Key Points

The aim is to characterize n-weak amenability for triangular Banach algebras without assumptions on the algebras involved.
Defined triangular Banach algebra for two algebras and a Banach module
Developed characterizations of n-weak amenability
Illustrated results with examples and comparisons to existing literature
Provided new characterizations of n-weak amenability
Showed that existing results can be derived with weaker assumptions
Presented examples where old methods failed to identify n-weak amenability

Abstract

For two Banach algebras A and B and a Banach (A, B) -module X, let Tri (A, X, B) be the corresponding triangular Banach algebra. In this paper, among other things, we give some characterizations of n-weak amenability of Tri (A, X, B), without any assumptions on A and B. We then apply our characterizations to obtain some of the known results in the literature with fewer assumptions and provide a direct proof. To illustrate our results we present some examples, where old results in the literature are not effective in identifying their n-weak amenability.

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