Open projections in operator algebras II: Compact projections

• Autorzy: David P. Blecher , Matthew Neal
• Języki publikacji: EN

Abstrakty

EN

We generalize some aspects of the theory of compact projections relative to a C*-algebra, to the setting of more general algebras. Our main result is that compact projections are the decreasing limits of 'peak projections', and in the separable case compact projections are just the peak projections. We also establish new forms of the noncommutative Urysohn lemma relative to an operator algebra, and we show that a projection is compact iff the associated face in the state space of the algebra is weak* closed.

Kategorie tematyczne

• 46L05: General theory of C * -algebras
• 46H10: Ideals and subalgebras
• 46L52: Noncommutative function spaces
• 47L30: Abstract operator algebras on Hilbert spaces
• 46L07: Operator spaces and completely bounded maps
• 46L85: Noncommutative topology
• 32T40: Peak functions
• 46L30: States

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 209
• Numer: 3
• Strony: 203-224

Daty

wydano

2012

Twórcy

autor

David P. Blecher

• Department of Mathematics, University of Houston, Houston, TX 77204-3008, U.S.A.

autor

Matthew Neal

• Department of Mathematics, Denison University, Granville, OH 43023, U.S.A.

Identyfikatory

DOI

10.4064/sm209-3-1