We consider a version of the notion of F -inverse semigroup (studied in the algebraic theory of inverse semigroups). We point out that an action of such an inverse semigroup on a locally compact space has associated a natural groupoid construction, very similar to the one of a transformation group. We discuss examples related to Toeplitz algebras on subsemigroups of discrete groups, to Cuntz-Kr...

We introduce the notion of the Fourier and Fouier-Stieltjes algebra of a topological ∗-semigroup and show that these are commutative Banach algebras. For a class of foundation semigroups, we show that these are preduals of von Neumann algebras. 1. Definitions and Notations Let S be a locally compact topological semigroup and M(S) be the Banach algebra of all bounded regular Borel measures μ on ...

We study inverse semigroup amalgams [S1, S2;U ], where S1 and S2 are finitely presented inverse semigroups with decidable word problem and U is an inverse semigroup with decidable membership problem in S1 and S2. We use a modified version of Bennett’s work on the structure of Schützenberger graphs of the R-classes of S1 ∗U S2 to state sufficient conditions for the amalgamated free products S1 ∗...

In this paper it is shown how the graphical methods developed by Stephen for analyzing inverse semigroup presentations may be used to study varieties of inverse semigroups. In particular, these methods may be used to solve the word problem for the free objects in the variety of inverse semigroups generated by the five-element combinatorial Brandt semigroup and in the variety of inverse semigrou...

This is a contribution to the theory of sums of independent random variables at an algebraico-analytical level: Let Prob∞(R) denote the convolution semigroup of all probability measures on R with all moments finite, topologized by polynomially weighted total variation. We prove that the cumulant sequence κ = (κ : ∈ N), regarded as a function from Prob∞(R) into the additive topological group R∞ ...

We argue that weak containment is an appropriate notion of amenability for inverse semigroups. Given an inverse semigroup S and a homomorphism φ of S onto a group G, we show, under an assumption on ker(φ), that S has weak containment if and only if G is amenable and ker(φ) has weak containment. Using Fell bundle amenability, we find a related result for inverse semigroups with zero. We show tha...

The symmetric inverse semigroup I(X) on a set X is the collection of all partial bijections between subsets with composition as algebraic operation. We study minimal Hausdorff topology I(X). present some characterizations it. When countable such Polish.