Vol. 65, No. 2, 1976

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The radical of a reflexive operator algebra

Alan Hopenwasser

Vol. 65 (1976), No. 2, 375–392
Abstract

The radical of a reflexive operator algebra A whose lattice of invariant subspaces L is commutative is related to the space of lattice homomorphisms of L onto {0,1}. To each such homomorphism ϕ is associated a closed, two-sided ideal Aϕ contained in A. The intersection of the Aϕ is contained in the radical; it is conjectured that equality always holds. The conjecture is proven for a variety of special cases: countable direct sums of nest algebras; finite direct sums of algebras which satisfy the conjecture; algebras whose lattice of invariant subspaces is finite; algebras whose lattice of invariant subspaces is isomorphic to the lattice of nonincreasing sequences with values in N ∪{∞}.

Mathematical Subject Classification 2000
Primary: 46L15, 46L15
Secondary: 47A15
Milestones
Received: 6 February 1976
Published: 1 August 1976
Authors
Alan Hopenwasser