On operator algebras containing cyclic Boolean algebras

Peter Michael Rosenthal and Ahmed Ramzy Sourour

Vol. 70 (1977), No. 1, 243–252

DOI: 10.2140/pjm.1977.70.243

Abstract

It is shown that a strongly closed algebra of operators which contains a σ-complete Boolean algebra with a cyclic vector and which has a totally-ordered invariant subspace lattice must be reflective.

Mathematical Subject Classification 2000

Primary: 46L20, 46L20

Secondary: 47A15

Milestones

Received: 18 February 1976

Published: 1 May 1977