On classifying monotone complete algebras of operators

Kazuyuki Saito, J D Maitland Wright

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We give a classificaion of "small" monotone complete C*-algebras by order properties. We construct a corresponding semigroup. This classification filters out von Neumann algebras; they are mapped to the zero of the classifying semigroup. We show that there are 2 to the power of the continuum distinct equivalence classes. This remains true when the clasification is restricted to special classes of monotone complete C*-algebras e.g. factors, injecive factors, injective operator systems and commutative algebras with separable structure space. Some examples and applications are given.
Original languageEnglish
Pages (from-to)321-355
Number of pages35
JournalRicerche di Matematica
Volume56
Issue number2
DOIs
Publication statusPublished - 20 Nov 2007

Fingerprint

Algebra
C*-algebra
Mathematical operators
Monotone
Semigroup
Commutative Algebra
Von Neumann Algebra
Operator
Equivalence class
Injective
Continuum
Filter
Distinct
Equivalence classes
Zero
Class

Keywords

  • monotone complete C*-algebras
  • operator algebras
  • semilattices

Cite this

On classifying monotone complete algebras of operators. / Saito, Kazuyuki; Wright, J D Maitland.

In: Ricerche di Matematica, Vol. 56, No. 2, 20.11.2007, p. 321-355.

Research output: Contribution to journalArticle

Saito, Kazuyuki ; Wright, J D Maitland. / On classifying monotone complete algebras of operators. In: Ricerche di Matematica. 2007 ; Vol. 56, No. 2. pp. 321-355.
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