Article
Operator Equations and Invariant Subspaces
Le Matematiche
Document Type
Article
Publication Date
1-1-1994
Disciplines
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.
Citation Information
Valentin Matache. "Operator Equations and Invariant Subspaces" Le Matematiche Vol. XLIX Iss. I (1994) p. 143 - 147 Available at: http://works.bepress.com/valentin-matache/16/
© 1995 Valentin Matache. This work is licensed under a Creative Commons Attribution-ShareAlike International 4.0 License, https://creativecommons.org/licenses/by/4.0/.