TY - JOUR
ID - 40529
TI - Uniform Convergence to a Left Invariance on Weakly Compact Subsets
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Ghaffari, Ali
AU - Javadi, Samaneh
AU - Tamimi, Ebrahim
AD - Department of Mathematics, Faculty of Science, University of Semnan, P.O.Box 35195-363, Semnan, Iran.
AD - Faculty of Engineering- East Guilan, University of Guilan, P. O. Box 44891-63157, Rudsar, Iran.
Y1 - 2020
PY - 2020
VL - 17
IS - 3
SP - 81
EP - 91
KW - Banach algebra
KW - $varphi$-amenability
KW - $varphi$-means
KW - Weak almost periodic
KW - Weak$^*$ topology
DO - 10.22130/scma.2019.100548.540
N2 - LetÂ $left{a_alpharight}_{alphain I}$ 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 $left{a_alpharight}_{alphain I}$ in $left{ain A; varphi(a)=1right}$ 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.
UR - http://scma.maragheh.ac.ir/article_40529.html
L1 - http://scma.maragheh.ac.ir/article_40529_52ec68cb33d86279de572c0696818129.pdf
ER -