A Semilinear Structure on Semigroups in a Metric Space

Springer Science and Business Media LLC - Tập 68 - Trang 419-444 - 2004
Rinaldo M. Colombo1, Andrea Corli2
1Department of Mathematics, University of Brescia, Italy
2Department of Mathematics, University of Ferrara, Italy

Tóm tắt

We introduce a sort of semilinear structure on subsets of the family of semigroups defined on a metric space. The key step is the definition of the sum of two semigroups, which is here achieved by means of the classical operator splitting technique. No linearity assumption is required, since the whole construction is in a metric space.