Weak Quasistability and Rajchman measures

TL;DR

This paper explores the relationship between weak quasistability, Rajchman measures, and operator properties, revealing that weak quasistability does not imply power boundedness and establishing links with measure theory.

Contribution

It demonstrates that weak quasistability does not imply power boundedness and characterizes weak quasistability of the position operator for finite continuous measures.

Findings

Weak quasistability does not imply power boundedness.

The position operator is weakly quasistable for every finite continuous measure.

Corollaries connect Rajchman measures with weak stability and quasistability.

Abstract

It is shown that weak quasistability does not imply power boundedness, but coercive power unbounded operators cannot be weakly quasistable.\ Although a finite measure over the unit disc is a Rajchman measure if and only if the position operator is weakly stable, it is shown that the position operator is weakly quasistable for every finite continuous measure over the unit disc.\ Corollaries linking Rajchman measures with weak stability and weak quasistability follow the above results.\