[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2010.23.2.305

ON LOCAL SPECTRAL PROPERTIES OF GENERALIZED SCALAR OPERATORS

Yoo, Jong-Kwang (Department of Liberal Arts and Science Chodang University)
Han, Hyuk (Department of Liberal Arts, Kongju National University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.23, no.2, 2010 , pp. 305-313 More about this Journal

Abstract

In this paper, we prove that if $T{\in}L$ (X) is a generalized scalar operator then Ker $T^p$ is the quasi-nilpotent part of T for some positive integer $p{\in}{\mathbb{N}}$ . Moreover, we prove that a generalized scalar operator with finite spectrum is algebraic. In particular, a quasi-nilpotent generalized scalar operator is nilpotent.

Keywords

quasi-nilpotent part; algebraic operator; generalized scalar operator;

Citations & Related Records

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