Arens regularity of certain weighted semigroup algebras and countability
B. Khodsiani, Ali Rejali, Hamid Reza Ebrahimi Vishki · arXiv (Cornell University) · 2015
It is known that every countable semigroup admits a weight w for which the semigroup algebra l_1(S,w) is Arens regular and no uncountable group admits such a weight; see [4]. In this paper, among other things, we show that for a large class of semigroups, the Arens regularity of the weighted semigroup algebra l_1(S,w) implies the countability of S.