Some remarks on the Helton class of an operator
Bull. Korean Math. Soc. 2009 Vol. 46, No. 3, 535-543
https://doi.org/10.4134/BKMS.2009.46.3.535
Printed May 1, 2009
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
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