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Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2011; 48(1): 183-195

Printed January 1, 2011

https://doi.org/10.4134/BKMS.2011.48.1.183

Copyright © The Korean Mathematical Society.

Inherited properties through the Helton class of an operator

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

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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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