Title : ( The bidual of a Banach algebra associated with a bilinear map )
Authors: Sedigheh Barootkoob , aminallah khosravi , Hamid Reza Ebrahimi Vishki ,
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Abstract
We associate a Banach algebra $\\\\\\\\\\\\\\\\A_\\\\\\\\\\\\\\\\Phi$ to each bounded bilinear map $\\\\\\\\\\\\\\\\Phi: \\\\\\\\\\\\\\\\X\\\\\\\\\\\\\\\\times \\\\\\\\\\\\\\\\Y\\\\\\\\\\\\\\\\rightarrow \\\\\\\\\\\\\\\\Z$ on Banach spaces, and we find out that this Banach algebra can be useful for many purposes in the theory of Banach algebras. For example, the construction of $\\\\\\\\\\\\\\\\A_\\\\\\\\\\\\\\\\Phi$ enables us to provide many simple examples of Banach algebras with different topological centers, which are neither Arens regular nor either left or right strongly Arens irregular. It also gives examples of Banach algebras which are not $n-$weakly amenable for each natural number $n.$ We also find out that the dual of $\\\\\\\\\\\\\\\\A_\\\\\\\\\\\\\\\\Phi$ does not enjoy the factorization property of any level.
Keywords
Bidual; Arens product; Bilinear map; Topological center; Weak amenability
@article{paperid:1074975,
author = {صدیقه باروط کوب and Khosravi, Aminallah and Ebrahimi Vishki, Hamid Reza},
title = {The bidual of a Banach algebra associated with a bilinear map},
journal = {Bolletino dell Unione Matematica Italiana},
year = {2019},
volume = {12},
number = {4},
month = {December},
issn = {1972-6724},
pages = {569--574},
numpages = {5},
keywords = {Bidual; Arens product; Bilinear map; Topological center; Weak amenability},
}
%0 Journal Article
%T The bidual of a Banach algebra associated with a bilinear map
%A صدیقه باروط کوب
%A Khosravi, Aminallah
%A Ebrahimi Vishki, Hamid Reza
%J Bolletino dell Unione Matematica Italiana
%@ 1972-6724
%D 2019
