Vol. 81, No. 2, 1979

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The carrier space of a reflexive operator algebra

Alan Hopenwasser and David Royal Larson

Vol. 81 (1979), No. 2, 417–434

Many properties of nest algebras are actually valid for reflexive operator algebras with a commutative subspace lattice. In this paper we collect a number of such results related to the carrier space of the algebra. Included among these results are a generalization of Ringrose’s criterion, a description of the partial correspondence between lattice homomorphisms of the carrier space and projections in the lattice, the construction of isometric representations of certain quotient algebras, and a direct sum decomposition of the commutant of the core modulo the intersection of the spectral ideals.

Mathematical Subject Classification 2000
Primary: 47D25, 47D25
Secondary: 47A15
Received: 23 September 1977
Published: 1 April 1979
Alan Hopenwasser
David Royal Larson