### 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 language | English |
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Pages (from-to) | 371-384 |

Number of pages | 14 |

Journal | Journal of Operator Theory |

Volume | 52 |

Issue number | 2 |

Publication status | Published - Oct 2004 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Shulman, V. S., & Todorov, I. (2004). On subspace lattices II. Continuity of Lat.

*Journal of Operator Theory*,*52*(2), 371-384.