Bicyclic semigroup

About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.

Distances between elements of a semigroup and estimates for derivatives

Abstract: This paper is concerned first with the behaviour of differences T(t)-T(s) near the origin, where (T(t)) is a semigroup of operators on a Banach space, defined either on the positive real line or a sector in the right half-plane (in which case it is assumed analytic). For the non-quasinilpotent case extensions of results in the published literature are provided, with best possible constants; in the case of quasinilpotent semigroups on the half-plane, it is shown that, in general, differences such as T(t)-T(2t) have norm approaching 2 near the origin. The techniques given enable one to derive estimates of other functions of the generator of the semigroup; in particular, conditions are given on the derivatives near the origin to guarantee that the semigroup generates a unital algebra and has bounded generator.

A Note on Locally Inverse Semigroup Algebras

Abstract: Let be a commutative ring and a finite locally inverse semigroup. It is proved that the semigroup algebra is isomorphic to the direct product of Munn algebras with , where is the number of -classes in , the number of -classes in , and a maximum subgroup of . As applications, we obtain the sufficient and necessary conditions for the semigroup algebra of a finite locally inverse semigroup to be semisimple.