Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2006; 43(2): 389-393

Printed June 1, 2006

Copyright © The Korean Mathematical Society.

Spectral continuity of essentially $p$[--]hyponormal operators

An-Hyun Kim and Eun-Young Kwon

Changwon National University, Changwon National University

Abstract

In this paper it is shown that the spectrum $\sigma$ is continuous at every $p$-hyponormal operator when restricted to the set of essentially $p$-hyponormal operators and moreover $\sigma$ is continuous when restricted to the set of compact perturbations of $p$-hyponormal operators whose spectral pictures have no holes associated with the index zero.

Keywords: spectrum, spectral radius, $p$-hyponormal operators, essentially $p$-hyponormal operators

MSC numbers: Primary 47A10, 47B20, 47B35