On subspace lattices II. Continuity of Lat

V.S. Shulman, Ivan Todorov

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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 Arvesonâ??s theorem on the reflexivity of commutative subspace lattices.
Original languageEnglish
Pages (from-to)371-384
Number of pages14
JournalJournal of Operator Theory
Volume52
Issue number2
Publication statusPublished - Oct 2004

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'On subspace lattices II. Continuity of Lat'. Together they form a unique fingerprint.

  • Cite this