Criteria for Algebraic Operators to be Unitary

Zenon Jan JabŁoński; Jan Stochel; Il Bong Jung*

doi:10.5666/KMJ.2022.63.1.1

Article

Kyungpook Mathematical Journal 2023; 63(1): 1-10

Published online March 31, 2023

Criteria for Algebraic Operators to be Unitary

Zenon Jan JabŁoński and Jan Stochel, Il Bong Jung*

Instytut Matematyki, Uniwersytet Jagielloński, ul. Łojasiewicza 6, PL-30348 Kraków, Poland
e-mail : Zenon.Jablonski@im.uj.edu.pl and Jan.Stochel@im.uj.edu.pl

Department of Mathematics, Kyungpook National University, Daegu 41566, Korea
e-mail : ibjung@knu.ac.kr

Received: July 5, 2022; Accepted: September 19, 2022

Abstract

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Abstract

Criteria for an algebraic operator T on a complex Hilbert space H to be unitary are established. The main one is written in terms of the convergence of sequences of the form {‖Tnh‖}n=0∞ with h∈H. Related questions are also discussed.

Keywords: Algebraic operator, unitary operator, normaloid operator, strong stability