Vol. 52, No. 1, 1974

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Self adjoint strictly cyclic operator algebras

Mary Rodriguez Embry

Vol. 52 (1974), No. 1, 53–57
Abstract

A strictly cyclic operator algebra 𝒜 on a Hilbert space X is a uniformly closed subalgebra of Z(X) such that 𝒜x0 = X for some x0 in X. In this paper it is shown that if 𝒜 is a strictly cyclic self-adjoint algebra, then (i) there exists a finite orthogonal decomposition of X,X = J=1n Mj, such that each Mj reduces 𝒜 and the restriction of 𝒜 to Mj is strongly dense in Z(Mj) and (ii) the commutant of 𝒜 is finite dimensional.

Mathematical Subject Classification 2000
Primary: 46L05
Milestones
Received: 6 October 1973
Revised: 30 January 1974
Published: 1 May 1974
Authors
Mary Rodriguez Embry