Ideals and hereditary subalgebras in operator algebras

Melahat Almus, David P. Blecher, and Charles John Read. "Ideals and hereditary subalgebras in operator algebras." Studia Mathematica 212.1 (2012): 65-93. <http://eudml.org/doc/285539>.

@article{MelahatAlmus2012,
abstract = {This paper may be viewed as having two aims. First, we continue our study of algebras of operators on a Hilbert space which have a contractive approximate identity, this time from a more Banach-algebraic point of view. Namely, we mainly investigate topics concerned with the ideal structure, and hereditary subalgebras (or HSA's, which are in some sense a generalization of ideals). Second, we study properties of operator algebras which are hereditary subalgebras in their bidual, or equivalently which are 'weakly compact'. We also give several examples answering natural questions that arise in such an investigation.},
author = {Melahat Almus, David P. Blecher, Charles John Read},
journal = {Studia Mathematica},
keywords = {operator algebras; one-sided ideals; hereditary subalgebra; approximate identity; semisimple algebra; semiprime algebra},
language = {eng},
number = {1},
pages = {65-93},
title = {Ideals and hereditary subalgebras in operator algebras},
url = {http://eudml.org/doc/285539},
volume = {212},
year = {2012},
}

TY - JOUR
AU - Melahat Almus
AU - David P. Blecher
AU - Charles John Read
TI - Ideals and hereditary subalgebras in operator algebras
JO - Studia Mathematica
PY - 2012
VL - 212
IS - 1
SP - 65
EP - 93
AB - This paper may be viewed as having two aims. First, we continue our study of algebras of operators on a Hilbert space which have a contractive approximate identity, this time from a more Banach-algebraic point of view. Namely, we mainly investigate topics concerned with the ideal structure, and hereditary subalgebras (or HSA's, which are in some sense a generalization of ideals). Second, we study properties of operator algebras which are hereditary subalgebras in their bidual, or equivalently which are 'weakly compact'. We also give several examples answering natural questions that arise in such an investigation.
LA - eng
KW - operator algebras; one-sided ideals; hereditary subalgebra; approximate identity; semisimple algebra; semiprime algebra
UR - http://eudml.org/doc/285539
ER -