Bulletin of the
Korean Mathematical Society
BKMS

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

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Bull. Korean Math. Soc. 2009; 46(3): 535-543

Printed May 1, 2009

https://doi.org/10.4134/BKMS.2009.46.3.535

Copyright © The Korean Mathematical Society.

Some remarks on the Helton class of an operator

Insook Kim, Yoenha Kim, Eungil Ko, and Ji Eun Lee

Ewha Women's University

Abstract

In this paper we study some properties of the Helton class of an operator. In particular, we show that the Helton class preserves the quasinilpotent property and Dunford's boundedness condition $(B)$. As corollaries, we get that the Helton class of some quadratically hyponormal operators or decomposable subnormal operators satisfies Dunford's boundedness condition $(B)$.

Keywords: Helton class, quasinilpotent property, Dunford's boundedness condition $(B)$

MSC numbers: Primary 47B20, Secondary 47A10