# PROPERTIES OF A κTH ROOT OF A HYPONORMAL OPERATOR

• Ko, Eun-Gil (Department of Mathematics, Ewha Women’s University)
• Published : 2003.11.01

#### Abstract

In this paper, we study some properties of (equation omitted) (defined below). In particular we show that an operator T $\in$(equation omitted) satisfying the translation invariant property is hyponormal and an invertible operator T $\in$ (equation omitted) and its inverse T$^{-1}$ have a common nontrivial invariant closed set. Also we study some cases which have nontrivial invariant subspaces for an operator in (equation omitted).

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#### Cited by

1. Continuity of the Sacker–Sell spectrum on the half line 2017, https://doi.org/10.1080/14689367.2017.1293613
2. On Analytic Roots of Hyponormal Operators vol.14, pp.5, 2017, https://doi.org/10.1007/s00009-017-0998-3
3. Continuity and Invariance of the Sacker–Sell Spectrum vol.28, pp.2, 2016, https://doi.org/10.1007/s10884-015-9515-1
4. On Some Normality-Like Properties and Bishop's Property () for a Class of Operators on Hilbert Spaces vol.2012, 2012, https://doi.org/10.1155/2012/975745