Universality and models for semigroups of operators on a Hilbert space

TL;DR

This paper investigates universal semigroups of operators on Hilbert spaces, providing criteria, examples, and models, especially for contraction and concave semigroups, extending Rota's concept of universality.

Contribution

It establishes criteria for universality of semigroups, offers specific examples, and develops models for concave semigroups using shifts on reproducing kernel Hilbert spaces.

Findings

Criteria for universality of semigroups are provided.

Examples of universal semigroups are given.

Models for concave semigroups are developed.

Abstract

This paper considers universal Hilbert space operators in the sense of Rota, and gives criteria for universality of semigroups in the context of uniformly continuous semigroups and contraction semigroups. Specific examples are given. Universal semigroups provide models for these classes of semigroups: following a line of research initiated by Shimorin, models for concave semigroups are developed, in terms of shifts on reproducing kernel Hilbert spaces.