Open projections in operator algebras II: Compact projections

Tom 209 / 2012

David P. Blecher, Matthew Neal Studia Mathematica 209 (2012), 203-224 MSC: Primary 46L07, 46L85, 47L30, 46L52; Secondary 32T40, 46H10, 46L05, 46L30. DOI: 10.4064/sm209-3-1

Streszczenie

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.

Autorzy

  • David P. BlecherDepartment of Mathematics
    University of Houston
    Houston, TX 77204-3008, U.S.A.
    e-mail
  • Matthew NealDepartment of Mathematics
    Denison University
    Granville, OH 43023, U.S.A.
    e-mail

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