Limiting absorption principle for contractions

TL;DR

This paper establishes limiting absorption principles for contractions on Hilbert spaces using positive commutator estimates, with applications to Toeplitz operators and quantum walks, impacting the analysis of discrete-time semigroups.

Contribution

It introduces new limiting absorption principles for contractions, expanding the theoretical framework with applications to quantum and operator theory.

Findings

Established limiting absorption principles for contractions.

Applied principles to Toeplitz operators and quantum walks.

Discussed implications for discrete-time semigroups.

Abstract

We establish limiting absorption principles for contractions on a Hilbert space. Our sufficient conditions are based on positive commutator estimates. We discuss the dynamical implications of this principle to the corresponding discrete-time semigroup and provide several applications. Notably to Toeplitz operators and contractive quantum walks.