PROBLEMS CONCERNING N-WEAK AMENABILITY OF A BANACH ALGEBRA


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Abstract

In this paper we extend the notion of n-weak amenability of a Banach algebra 𝒜 when n ∈ ℕ. Technical calculations show that when 𝒜 is Arens regular or an ideal in 𝒜**, then 𝒜* is an 𝒜(2n)-module and this idea leads to a number of interesting results on Banach algebras. We then extend the concept of n-weak amenability to n ∈ ℤ.

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