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.
Insook Kim, Yoenha Kim, Eungil Ko, and Ji Eun Lee
Ewha Women's University
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
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