Journal of Operator Theory

Volume 52, Issue 2, Fall 2004 pp. 371-384.

On subspace lattices. II. Continuity of Lat

Authors: V.S. Shulman (1) and I.G. Todorov (2)
Author institution: (1) School of Communications Technologies and Mathematical Sciences, University of North London, Holloway, London N7 8DB, UK
(2) Department of Pure Mathematics, Queen's University Belfast, Belfast, BT7 1NN Northern Ireland, Northern Ireland, UK

Summary: We study the continuity of the map Lat sending an ultraweakly closed operator algebra to its invariant subspace lattice. We provide an example showing that Lat is in general discontinuous and give sufficient conditions for the restricted continuity of this map. As consequences we obtain that Lat is continuous on the classes of von Neumann and Arveson algebras and give a general approximative criterion for reflexivity, which extends Arveson's theorem on the reflexivity of commutative subspace lattices.

Keywords: subspace lattices, continuity, reflexivity, operator algebras

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