IDEAL STRUCTURE AND C-ALGEBRAS OF LOW RANK

IDEAL STRUCTURE AND C-ALGEBRAS OF LOW RANK

We explore various constructions with ideals in a C*-algebra A in relation to the notions of real rank, stable rank and extremal richness. In particular we investigate the maximum ideals of low rank. And we investigate the relationship between existence of infinite or properly infinite projections i...

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Veröffentlicht in:Mathematica scandinavica 2007-01, Vol.100 (1), p.4-33
Hauptverfasser: BROWN, LAWRENCE G., PEDERSEN, GERT K.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Approximation
Graphical evaluation and review technique
Mathematical theorems
Mathematics
Morphisms
Operator theory
Quotients
Unit ball
Von Neumann algebra
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Zusammenfassung:We explore various constructions with ideals in a C*-algebra A in relation to the notions of real rank, stable rank and extremal richness. In particular we investigate the maximum ideals of low rank. And we investigate the relationship between existence of infinite or properly infinite projections in an extremally rich C*-algebra and non-existence of ideals or quotients of stable rank one.
ISSN:0025-5521
1903-1807