Criteria for algebraic operators to be unitary

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 $\{\Vert T^{n}h\Vert {\}}_{n=0}^{\infty }$ with $h\in \mathcal{H}$. Related questions are also discussed.

9 pages