H. D. Junghenn

Compact right topological semigroups and generalizations of almost periodicity

Preliminaries.- The structure of compact semigroups.- Subspaces of C(S) and compactifications of S.- Fixed points and left invariant means on subspaces of C(S).- Examples.

DISTAL COMPACTIFICATIONS OF SEMIGROUPS

Properties of distal functions on semitopological semigroups are studied via the device of right topological semigroup compactification. Algebras of distal functions are used to construct the universal right simple, left simple, and group compactifications of a semigroup, and these compactifications are in turn systemati- cally employed to obtain information about distal functions. Applications are made to semidirect products and flows.

Operator Semigroup Compactifications

A weakly continuous, equicontinuous representation of a semitopological semigroup S on a locally convex topological vector space X gives rise to a family of operator semigroup compactifications of S, one for each invariant subspace of X. We consider those invariant subspaces which are maximal with respect to the associated compactification possessing a given property of semigroup compactifications and show that under suitable hypotheses this maximality is preserved under the formation of projective limits, strict inductive limits and tensor products.

Amenability of function spaces on thick subsemigroups

Let F be a translation invariant left introverted algebra of bounded continuous real-valued functions on a semigroup S. Various equivalent versions of the notion of F-left thickness of a subsemigroup T are presented, and the relationship between the left amenability of F and that of FI T is examined.

Almost periodic compactifications of group extensions

AbstractLet

Analysis on semigroups : function spaces, compactifications, representations

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Semigroup compactifications of semidirect products

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