Bolletino dell Unione Matematica Italiana, Year (2019-2)

#### Title : ( The bidual of a Banach algebra associated with a bilinear map )

Authors: Sedigheh Barootkoob , aminallah khosravi , Hamid Reza Ebrahimi Vishki ,

Citation: BibTeX | EndNote

#### 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
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@article{paperid:1074975,
author = {Sedigheh Barootkoob 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},
month = {February},
issn = {1972-6724},
keywords = {Bidual; Arens product; Bilinear map; Topological center; Weak amenability},
}