Primitive idempotent measures on compact semitopological semigroups

Idempotent Measures on Compact Semigroups

Throughout this paper, 5 will be a compact Hausdorff topological semigroup, 5 will denote the convolution semigroup of normalized non-negative regular Borel measures on 5, and H will be the carrier of a measure p in 5. The space of continuous complex valued functions on 5 will be denoted by C(S), while Cr(S) will be the subspace of C(S) of real valued functions. Standard terminology and definit...

On supermatrix idempotent operator semigroups

One-parameter semigroups of antitriangle idempotent supermatrices and corresponding superoperator semigroups are introduced and investigated. It is shown that t-linear idempotent superoperators and exponential superoperators are mutually dual in some sense, and the first gives additional to exponential solution to the initial Cauchy problem. The corresponding functional equation and analog of r...

On the Structure of Certain Idempotent Semigroups

Some general theorems concerning residual finiteness of algebras are given that are applied to show that every idempotent semigroup satisfying xyzx = xzyx identically is a subcartesian product of certain simple semigroups of order two and three. Introduction. In this paper we present a technique involving a special type of infinitely long sentence which seems of fairly general applicability in ...

The universal $mathcal{AIR}$- compactification of a semigroup

In this paper we establish a characterization of abelian compact Hausdorff semigroups with unique idempotent and ideal retraction property. We also introduce a function algebra on a semitopological semigroup whose associated semigroup compactification is universal withrespect to these properties.

Functions of bounded variation on idempotent semigroups