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Invariant Subspaces for Semigroups of Algebraic Operators

✍ Scribed by Grega Cigler; Roman Drnovšek; Damjana Kokol-Bukovšek; Matjaž Omladič; Thomas J. Laffey; Heydar Radjavi; Peter Rosenthal

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
239 KB
Volume
160
Category
Article
ISSN
0022-1236

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✦ Synopsis

269 305) that a semigroup of matrices is triangularizable if the ranks of all the commutators of elements of the semigroup are at most 1. Our main theorem is an extension of this result to semigroups of algebraic operators on a Banach space. We also obtain a related theorem for a pair [A, B] of arbitrary bounded operators satisfying rank (AB&BA)=1 and several related conditions. In addition, it is shown that a semigroup of algebraically unipotent operators of bounded degree is triangularizable.

1998 Academic Press

1. Introduction

The following definition has been studied in both the finite-dimensional and the infinite-dimensional contexts.

Definition. A collection of bounded linear operators on a complex Banach space is triangularizable if there is a chain of subspaces which is article no. FU983293

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