Weak limit semigroup in operator theory and ergodic theory

TL;DR

This paper investigates the structure of weak limit semigroups of operators across various contexts, including measure-preserving transformations and Hilbert space operators, emphasizing the identification of large subsets in the generic case.

Contribution

It provides a comprehensive analysis of weak limit semigroups for different classes of operators, highlighting the conditions under which large subsets can be characterized.

Findings

Identifies large subsets of weak limit semigroups in measure-preserving and Hilbert space contexts.

Analyzes the generic case for weak limit semigroups across different operator classes.

Abstract

We study the weak limit semigroup of an operator $T$, i.e., the set of all operators being weak limit points of the powers of $T$, in three different but related contexts: Koopman operators of measure-preserving transformations, contractions/isometries/unitaries on separable Hilbert spaces and positive operators on $L^p$-spaces. Hereby we focus on finding large subsets of the weak limit semigroup, in particular in the generic case.