@article {
author = {Ghaffari, Ali and Javadi, Samaneh and Tamimi, Ebrahim},
title = {Uniform Convergence to a Left Invariance on Weakly Compact Subsets},
journal = {Sahand Communications in Mathematical Analysis},
volume = {17},
number = {3},
pages = {81-91},
year = {2020},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2019.100548.540},
abstract = {LetÂ $\left\{a_\alpha\right\}_{\alpha\in I}$ be a bounded net in a Banach algebra $A$ and $\varphi$ a nonzero multiplicative linear functional on $A$. In this paper, we deal with the problem of when $\|aa_\alpha-\varphi(a)a_\alpha\|\to0$ uniformly for all $a$ in weakly compact subsets of $A$. We show that Banach algebras associated to locally compact groups suchÂ as Segal algebras and $L^1$-algebras are responsive to this concept. It is also shown that $Wap(A)$ has a left invariant $\varphi$-mean if and only if there exists a bounded net $\left\{a_\alpha\right\}_{\alpha\in I}$ in $\left\{a\in A;\ \varphi(a)=1\right\}$ such that $\|aa_\alpha-\varphi(a)a_\alpha\|_{Wap(A)}\to0$ uniformly for all $a$ in weakly compact subsets of $A$. Other results in this direction are also obtained.},
keywords = {Banach algebra,$varphi$-amenability,$varphi$-means,Weak almost periodic,Weak$^*$ topology},
url = {http://scma.maragheh.ac.ir/article_40529.html},
eprint = {http://scma.maragheh.ac.ir/article_40529_52ec68cb33d86279de572c0696818129.pdf}
}