Ideal Module Amenability of Triangular Banach Algebras
DOI:
https://doi.org/10.18311/jims/2019/21637Keywords:
Ideal module amenability, Inverse semigroup algebras, Module amenability, Triangular Banach algebrasAbstract
Let A and B be unital Banach algebras and M be an unital Banach A,B-module. In this paper we define the concept of the (n)-ideal module amenability of Banach algebras and investigate the relation between the (2n-1)-ideal module amenability of triangular Banach algebra Τ = [A M B] (as a Τ = {[α α] : α ∈u}-module) and (2n - 1)-ideal module amenability of A and B (as an u-module), where u is a (not necessarily unital) Banach algebra such that A, B and M are commutative Banach u-bimodules. Finally, in the case that A = B = M = l1(S) and u = l1(E), for unital and commutative inverse semigroup S with idempotent set E, we show that T as an u-module is (2n - 1)- ideal module amenable while is not module amenable.Downloads
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Copyright (c) 2019 Ebrahim Nasrabadi
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This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2019-03-18
Published 2019-08-22
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