IJPAM: Volume 120, No. 3 (2018)

Title

CYCLIC MODULE AMENABILITY OF BANACH ALGEBRAS

Authors

M.R. Miri$^1$, E. Nasrabadi$^2$, M.H. Rezaei Gol$^3$
$^{1, 2, 3}$Faculty of Mathematics Science and Statistics
University of Birjand
Birjand 9717851367, IRAN

Abstract

In this paper, we define the concept of cyclic module amenability for Banach algebras and we study the hereditary properties of cyclic module amenability on Banach algebras. For example, we investigate relationship between cyclic module amenability of $I$, $A/I$ and $A$, where $I$ is closed ideal and $\mathfrak{A}$-submodule of $A$. Also it is shown that cyclic module amenability of $A$ and $B$ follows from cyclic module amenability of $A\oplus_{\ell^1} B$ and cyclic module amenability of $A$ and $B$ implies cyclic module amenability of $A\oplus_{\ell^1} B$, if $A$ and $B$ are essential.

History

Received: February 27, 2018
Revised: August 23, 2018
Published: November 10, 2018

AMS Classification, Key Words

AMS Subject Classification: 43A07, 46H25, 46H35
Key Words and Phrases: cyclic derivation, cyclic module derivation, cyclic amenability, cyclic module amenability, weak module amenability

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How to Cite?

DOI: 10.12732/ijpam.v120i3.3 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 120
Issue: 3
Pages: 315 - 327


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