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 language | English |
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Pages (from-to) | 321-355 |
Number of pages | 35 |
Journal | Ricerche di Matematica |
Volume | 56 |
Issue number | 2 |
DOIs | |
Publication status | Published - 20 Nov 2007 |
Keywords
- monotone complete C*-algebras
- operator algebras
- semilattices