Embedding of some classes of operators into strongly continuous semigroups

TL;DR

This paper investigates when certain classes of operators, like composition and Toeplitz operators on Hardy space, can be embedded into strongly continuous semigroups, providing characterizations and conditions for isometric cases.

Contribution

It offers new characterizations for embedding composition and Toeplitz operators into strongly continuous semigroups, especially focusing on isometric operators using existing conditions.

Findings

Characterizations for embedding composition and Toeplitz operators.

Necessary and sufficient conditions for isometric operators.

Application of T. Eisner's condition to specific operator classes.

Abstract

In this paper we study the embedding problem of an operator into a strongly continuous semigroup. We obtain characterizations for some classes of operators, namely composition operators and analytic Toeplitz operators on the Hardy space H^2. In particular, we focus on the isometric ones using the necessary and sufficient condition observed by T. Eisner.