Tensor products of subspace lattices and rank one density

Savvas Papapanayides, Ivan G. Todorov

Research output: Contribution to journalArticle

Abstract

We show that, if M is a subspace lattice with the property that the rank one subspace of its operator algebra is weak* dense, L is a commutative subspace lattice and P is the lattice of all projections on a separable Hilbert space, then L⊗M⊗P is reflexive. If M is moreover an atomic Boolean subspace lattice while L is any subspace lattice, we provide a concrete lattice theoretic description of L⊗M in terms of projection valued functions defined on the set of atoms of M . As a consequence, we show that the Lattice Tensor Product Formula holds for AlgM and any other reflexive operator algebra and give several further corollaries of these results.
Original languageEnglish
Pages (from-to)175-189
JournalIntegral Equations and Operator Theory
Volume79
Issue number2
Early online date28 Mar 2014
Publication statusPublished - Jun 2014

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