PROPERTIES OF A κTH ROOT OF A HYPONORMAL OPERATOR

Title & Authors
PROPERTIES OF A κTH ROOT OF A HYPONORMAL OPERATOR
Ko, Eun-Gil;

Abstract
In this paper, we study some properties of (equation omitted) (defined below). In particular we show that an operator T $\small{\in}$(equation omitted) satisfying the translation invariant property is hyponormal and an invertible operator T $\small{\in}$ (equation omitted) and its inverse T$\small{^{-1}}$ have a common nontrivial invariant closed set. Also we study some cases which have nontrivial invariant subspaces for an operator in (equation omitted).
Keywords
hyponormal operators;hypercyclicity;subscalarity;
Language
English
Cited by
1.
Continuity of the Sacker–Sell spectrum on the half line, Dynamical Systems, 2017, 1
2.
On Analytic Roots of Hyponormal Operators, Mediterranean Journal of Mathematics, 2017, 14, 5
3.
Continuity and Invariance of the Sacker–Sell Spectrum, Journal of Dynamics and Differential Equations, 2016, 28, 2, 533
4.
On Some Normality-Like Properties and Bishop's Property () for a Class of Operators on Hilbert Spaces, International Journal of Mathematics and Mathematical Sciences, 2012, 2012, 1
References
1.
J. Funct. Anal., 1995. vol.128. pp.374-383

2.
Theory of generalized spectral operators, 1968.

3.
Subnormal operators, 1981.

4.
Arch. Math., 1989. vol.52. pp.562-570

5.
A Hilbert space problem book, 1982.

6.
Ph.D Thesis, Univ. of Toronto, 1982.

7.
Glasgow Math. J., 1999. vol.41. pp.463-470

8.
Proc. Amer. Math. Soc., 1995. vol.123. pp.3473-3481

9.
Bull. Korean Math. Soc., 1996. vol.33. 1, pp.29-33

10.
Lectures on hyponormal operators, 1989.

11.
J. Operator Th., 1984. vol.12. pp.385-395

12.
Math. Zeit., 1970. vol.116. pp.323-330

13.
J. Math. Anal. Appl., 1971. vol.34. pp.653-664

14.
Pacific J. Math., 1962. vol.12. pp.1453-1458