Operator equations and invariant subspaces

  • Valentin Matache
Keywords: Invariant subspaces, Hyperinvariant subspaces

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 nontrivial 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.

Published
1995-03-01
Section
Articoli