Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2011; 48(6): 1129-1135

Printed November 1, 2011

https://doi.org/10.4134/BKMS.2011.48.6.1129

Copyright © The Korean Mathematical Society.

Some invariant subspaces for subscalar operators

Jong-Kwang Yoo

Chodang University

Abstract

In this note, we prove that every subscalar operator with finite spectrum is algebraic. In particular, a quasi-nilpotent subscalar operator is nilpotent. We also prove that every subscalar operator with property $(\delta)$ on a Banach space of dimension greater than 1 has a non-trivial invariant closed linear subspace.

Keywords: algebraic spectral subspace, analytic spectral subspace, decomposable operator, invariant subspaces property $(\beta)$, property $(\delta),$ subscalar operator

MSC numbers: Primary 47A11, 47A53

Stats or Metrics

Share this article on :

Related articles in BKMS