@article {
author = {Hayati, Bahman},
title = {Completely Continuous Banach Algebras},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {10},
number = {1},
pages = {55-62},
year = {2019},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2019.1184.1268},
abstract = {For a Banach algebra $\mathfrak{A}$, we introduce ~$c.c(\mathfrak{A})$, the set of all $\phi\in \mathfrak{A}^*$ such that $\theta_\phi:\mathfrak{A}\to \mathfrak{A}^*$ is a completely continuous operator, where $\theta_\phi$ is defined by $\theta_\phi(a)=a\cdot\phi$ for all $a\in \mathfrak{A}$. We call $\mathfrak{A}$, a completely continuous Banach algebra if $c.c(\mathfrak{A})=\mathfrak{A}^*$. We give some examples of completely continuous Banach algebras and a sufficient condition for an open problem raised for the first time by J.E Gale, T.J. Ransford and M. C. White: Is there exist an infinite-dimensional amenable Banach algebra whose underlying Banach space is reflexive? We prove that a reflexive, amenable, completely continuous Banach algebra with the approximation property is trivial.},
keywords = {Amenability,Completely continuous,Banach algebra},
url = {https://ijnaa.semnan.ac.ir/article_4052.html},
eprint = {https://ijnaa.semnan.ac.ir/article_4052_98d6bd83d5d5695668206e7b12bb7f92.pdf}
}