Vol. 49, No. 1, 1973

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Maximal invariant subspaces of strictly cyclic operator algebras

Mary Rodriguez Embry

Vol. 49 (1973), No. 1, 45–50
Abstract

A stricily cyclic operator algebra 𝒜 on a complex Banach space X(dimX 2) is a uniformly closed subalgebra of (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),AzI 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
Authors
Mary Rodriguez Embry