Ideal Module Amenability of Triangular Banach Algebras

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Authors

  • Ebrahim Nasrabadi
     Faculty of Mathematics Science and Statistic, University of Birjand, Birjand ,IR

DOI:

https://doi.org/10.18311/jims/2019/21637

Keywords:

Ideal module amenability, Inverse semigroup algebras, Module amenability, Triangular Banach algebras
Primary 46H20, Secondary 46H25, 16E40.

Abstract

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.

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Published

2019-08-22

How to Cite

Nasrabadi, E. (2019). Ideal Module Amenability of Triangular Banach Algebras. The Journal of the Indian Mathematical Society, 86(3-4), 272–285. https://doi.org/10.18311/jims/2019/21637

Issue

Volume 86, Issue 3-4, July-December 2019

Section

Articles

License

Copyright (c) 2019 Ebrahim Nasrabadi

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2018-07-25
Accepted 2019-03-18
Published 2019-08-22

 

References

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