Inherited properties through the Helton class of an operator
Bull. Korean Math. Soc. 2011 Vol. 48, No. 1, 183-195
Printed January 1, 2011
Insook Kim, Yoenha Kim, Eungil Ko, and Ji Eun Lee
Ewha Women's University, Ewha Women's University, Ewha Women's University, Ewha Women's University
Abstract : In this paper we show that Helton class preserves the nilpotent and finite ascent properties. Also, we show some relations on nontransitivity and decomposability between operators and their Helton classes. Finally, we give some applications in the Helton class of weighted shifts.
Keywords : Helton class, nilpotent property, finite ascent property, essential spectra, decomposability
MSC numbers : Primary 47B20; Secondary 47A10
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