Journal of Operator Theory

Volume 61, Issue 2, Spring 2009 pp. 253-278.

Normality via local spectral radii

Authors: Dariusz Cichon (1), Il Bong Jung (2), and Jan Stochel (3)
Author institution: (1) Instytut Matematyki, Uniwersytet Jagiellonski, ul. Reymonta 4, PL-30059 Krakow, Poland
(2) Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu 702-701, Korea
(3) Instytut Matematyki, Uniwersytet Jagiellonski, ul. Reymonta 4, PL-30059 Krakow, Poland

Summary: A new criterion for essential normality of unbounded Hilbert space operators is furnished in terms of local spectral radius. Accordingly, extensive study of operators of certain types related to local spectral radius is conducted. Spectral radii of local restrictions of a normal operator are investigated.

Keywords: Local spectral radius, normal operator, paranormal operator, normaloid operator, algebraic operator, locally algebraic operator, compact operator

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