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Restricted algebras on inverse semigroups. I: Representation theory. (English) Zbl 1106.43002
Summary: The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the first in a series of papers in which we have investigated a similar relation on inverse semigroups. We use a new concept of “restricted” representations and study the restricted semigroup algebras and corresponding $C^*$-algebras.

##### MSC:
 43A35 Positive definite functions on groups, semigroups, etc. 43A20 $L^1$-algebras on groups, semigroups, etc.
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