Open projections in operator algebras II: Compact projections

David P. Blecher, and Matthew Neal. "Open projections in operator algebras II: Compact projections." Studia Mathematica 209.3 (2012): 203-224. <http://eudml.org/doc/285860>.

@article{DavidP2012,
abstract = {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.},
author = {David P. Blecher, Matthew Neal},
journal = {Studia Mathematica},
keywords = {non-self-adjoint operator algebras; open projection; closed projection; compact projection; faces; semi-exposed faces; ideals; noncommutative Urysohn lemma; hereditary subalgebra},
language = {eng},
number = {3},
pages = {203-224},
title = {Open projections in operator algebras II: Compact projections},
url = {http://eudml.org/doc/285860},
volume = {209},
year = {2012},
}

TY - JOUR
AU - David P. Blecher
AU - Matthew Neal
TI - Open projections in operator algebras II: Compact projections
JO - Studia Mathematica
PY - 2012
VL - 209
IS - 3
SP - 203
EP - 224
AB - 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.
LA - eng
KW - non-self-adjoint operator algebras; open projection; closed projection; compact projection; faces; semi-exposed faces; ideals; noncommutative Urysohn lemma; hereditary subalgebra
UR - http://eudml.org/doc/285860
ER -