Arens regularity of certain weighted semigroup algebras and countability
Abstract
It is known that every countable semigroup admits a weight w for which the semigroup algebra l1(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 l1(S,w) implies the countability of S.
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