Operator Equations and Invariant Subspaces

Authors

Valentin Matache, University of Nebraska at OmahaFollow

Document Type

Article

Publication Date

1994

Publication Title

Le Matematiche

Volume

XLIX

Issue

I

First Page

143

Last Page

147

Abstract

Banach space operators acting on some fixed space X are considered. If two such operators A and B verify the condition A² = B² and if A has non-trivial hyperinvariant subspaces, then B has nontrivial invariant subspaces. If A and B commute and satisfy a special type of functional equation, and if A is not a scalar multiple of the identity, the author proves that if A has nontrivial invariant subspaces, then so does B.

Comments

© 1995 Valentin Matache. This work is licensed under a Creative Commons Attribution-ShareAlike International 4.0 License, https://creativecommons.org/licenses/by/4.0/.

Recommended Citation

Matache, Valentin, "Operator Equations and Invariant Subspaces" (1994). Mathematics Faculty Publications. 28.
https://digitalcommons.unomaha.edu/mathfacpub/28