A semigroup of operators in convexity theory

A semigroup of operators in convexity theory

We consider three operators which appear naturally in convexity theory and determine completely the structure of the semigroup generated by them.

Pseudodifferential operators associated with a semigroup of operators

Hypercyclic Behaviour of Operators in a Hypercyclic C0-Semigroup

Let {Tt}t≥0 be a hypercyclic strongly continuous semigroup of operators. Then each Tt (t > 0) is hypercyclic as a single operator, and it shares the set of hypercyclic vectors with the semigroup. This answers in the affirmative a natural question concerning hypercyclic C0-semigroups. The analogous result for frequent hypercyclicity is also obtained.

Profinite Methods in Semigroup Theory

A highlight of the Conference held at the University of Nebraska-Lincoln in May 2000 was the proof of the decidability of the complexity of nite semigroups and automata, presented by Rhodes 78]. This problem had been open for more than thirty years and had inspired many active branches of semigroup theory. As is usually the case with old and diicult problems, the solution for the original quest...

Geometric Semigroup Theory

Geometric semigroup theory is the systematic investigation of finitely-generated semigroups using the topology and geometry of their associated automata. In this article we show how a number of easily-defined expansions on finite semigroups and automata lead to simplifications of the graphs on which the corresponding finite semigroups act. We show in particular that every finite semigroup can b...