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Open projections in operator algebras II: Compact projections
David P. Blecher1 ; Matthew Neal2
1 Department of Mathematics University of Houston Houston, TX 77204-3008, U.S.A.
2 Department of Mathematics Denison University Granville, OH 43023, U.S.A.
Studia Mathematica, Tome 209 (2012) no. 3, pp. 203-224

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm209-3-1
Keywords: generalize aspects theory compact projections relative * algebra setting general algebras main result compact projections decreasing limits peak projections separable compact projections just peak projections establish forms noncommutative urysohn lemma relative operator algebra projection compact associated face state space algebra weak * closed

David P. Blecher 1 ; Matthew Neal 2

1 Department of Mathematics University of Houston Houston, TX 77204-3008, U.S.A.
2 Department of Mathematics Denison University Granville, OH 43023, U.S.A. 
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David P. Blecher; Matthew Neal. Open projections in operator algebras II:
 Compact projections. Studia Mathematica, Tome 209 (2012) no. 3, pp. 203-224. doi: 10.4064/sm209-3-1

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