Vol. 39, No. 3, 1971

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Strictly cyclic operator algebras

Alan Leslie Lambert

Vol. 39 (1971), No. 3, 717–726

This paper is concerned with the structure of abelian algebras.𝒜 of operators on Hilbert space such that 𝒜x = for some vector x in H. It is shown that if a transitive algebra 𝒯 contains such an algebra then F is dense in the weak topology on (). It is also shown that when an algebra of this type is semi-simple then it is a reflexive operator algebra. The algebras investigated have the property that every densely defined linear trans-formation commuting with the algebra is bounded.

Mathematical Subject Classification 2000
Primary: 46L15
Secondary: 47A15
Received: 28 September 1970
Published: 1 December 1971
Alan Leslie Lambert