PARTIAL INVERSE SEMIGROUP $C^*$-ALGEBRA

Abstract

The notion of partial group $C^{*}$-algebra of a discrete group introduced by R. Exel in [3] is generalized to an idempotent unital inverse semigroup, and the partial inverse semigroup $C^{*}$-algebra is defined. By using the algebras of multipliers of ideals of an associative algebra, we can prove some theorem in the $C^{*}$-algebra context without using the approximate identity.