PARACLOSED INVARIANT SUBSPACES OF A BANACH SPACE

by Matjaž Omladič, Ljubljana, Slovenia

Abstract. The notion of paratransitivity for a set of bounded operators on a Banach space is introduced. For a nonparatransitive algebra of operators sufficient conditions are given to be transitive. The result is strong enough to imply the known equivalence of both transitivities for a strongly closed algebra of operators on a Hilbert space, containing a maximal abelian C^{∗} algebra. Mathematics subject classification: 47A15 Keywords: Invariant operator ranges, Banach spaces, transitiveness.