Criteria for algebraic operators to be unitary

TL;DR

This paper establishes criteria for when algebraic operators on complex Hilbert spaces are unitary, focusing on the convergence of sequences involving operator powers, and discusses related questions.

Contribution

It introduces new criteria based on sequence convergence for determining unitarity of algebraic operators on Hilbert spaces.

Findings

Criteria involving sequence convergence for unitarity

Conditions expressed in terms of operator powers

Discussion of related algebraic questions

Abstract

Criteria for an algebraic operator $T$ on a complex Hilbert space $\mathcal{H}$ to be unitary are established. The main one is written in terms of the convergence of sequences of the form $\{\|T^nh\|\}_{n=0}^{\infty}$ with $h\in \mathcal{H}$. Related questions are also discussed.