On the weak analogue of the Trotter-Kato theorem

TL;DR

This paper investigates the weak operator topology analogue of the Trotter-Kato theorem for C_0-semigroups on Banach spaces, analyzing the conditions under which the classical results hold in this weaker topology.

Contribution

It introduces and examines the weak operator topology version of the Trotter-Kato theorem, extending understanding of semigroup approximations in Banach spaces.

Findings

Identifies conditions where the weak topology version holds

Clarifies limitations of weak operator topology in semigroup approximation

Provides insights into operator topology implications for semigroup theory

Abstract

In the Trotter-Kato approximation theorem for C_0-semigroups on Banach spaces, we replace the strong by the weak operator topology and discuss the validity of the relevant implications.