Maximal invariant subspaces of strictly cyclic operator algebras

Mary Rodriguez Embry

Vol. 49 (1973), No. 1, 45–50

DOI: 10.2140/pjm.1973.49.45

Abstract

A stricily cyclic operator algebra 𝒜 on a complex Banach space X(dimX ≧ 2) is a uniformly closed subalgebra of ℒ(X) such that 𝒜x = X for some x in X. In this paper it is shown that (i) if 𝒜 is strictly cyclic and intransitive, then 𝒜 has a maximal (proper, closed) invariant subspace and (ii) if A ∈ℒ(X),A≠zI and {A}′ (the commutant of A) is strictly cyclic, then A has a maximal hyperinvariant subspace.

Mathematical Subject Classification 2000

Primary: 47A15

Secondary: 46L20

Milestones

Received: 14 July 1972

Revised: 25 August 1972

Published: 1 November 1973