Open projections in operator algebras I: Comparison theory

David P. Blecher, and Matthew Neal. "Open projections in operator algebras I: Comparison theory." Studia Mathematica 208.2 (2012): 117-150. <http://eudml.org/doc/285770>.

@article{DavidP2012,
abstract = {We begin a program of generalizing basic elements of the theory of comparison, equivalence, and subequivalence, of elements in C*-algebras, to the setting of more general algebras. In particular, we follow the recent lead of Lin, Ortega, Rørdam, and Thiel of studying these equivalences, etc., in terms of open projections or module isomorphisms. We also define and characterize a new class of inner ideals in operator algebras, and develop a matching theory of open partial isometries in operator ideals which simultaneously generalize the open projections in operator algebras (in the sense of the authors and Hay), and the open partial isometries (tripotents) introduced by the authors.},
author = {David P. Blecher, Matthew Neal},
journal = {Studia Mathematica},
keywords = {TRO; JB-triples; Hilbert -module; nonselfadjoint operator algebra; open projection; Cuntz semigroup; comparison theory; equivalence relations on an operator algebra; hereditary subalgebra; ideal; partial isometry},
language = {eng},
number = {2},
pages = {117-150},
title = {Open projections in operator algebras I: Comparison theory},
url = {http://eudml.org/doc/285770},
volume = {208},
year = {2012},
}

TY - JOUR
AU - David P. Blecher
AU - Matthew Neal
TI - Open projections in operator algebras I: Comparison theory
JO - Studia Mathematica
PY - 2012
VL - 208
IS - 2
SP - 117
EP - 150
AB - We begin a program of generalizing basic elements of the theory of comparison, equivalence, and subequivalence, of elements in C*-algebras, to the setting of more general algebras. In particular, we follow the recent lead of Lin, Ortega, Rørdam, and Thiel of studying these equivalences, etc., in terms of open projections or module isomorphisms. We also define and characterize a new class of inner ideals in operator algebras, and develop a matching theory of open partial isometries in operator ideals which simultaneously generalize the open projections in operator algebras (in the sense of the authors and Hay), and the open partial isometries (tripotents) introduced by the authors.
LA - eng
KW - TRO; JB-triples; Hilbert -module; nonselfadjoint operator algebra; open projection; Cuntz semigroup; comparison theory; equivalence relations on an operator algebra; hereditary subalgebra; ideal; partial isometry
UR - http://eudml.org/doc/285770
ER -