Closed ideals in the Banach algebra of operators on a Banach space

Niels Jakob Laustsen, and Richard J. Loy. "Closed ideals in the Banach algebra of operators on a Banach space." Banach Center Publications 67.1 (2005): 245-264. <http://eudml.org/doc/286174>.

@article{NielsJakobLaustsen2005,
abstract = {In general, little is known about the lattice of closed ideals in the Banach algebra ℬ(E) of all bounded, linear operators on a Banach space E. We list the (few) Banach spaces for which this lattice is completely understood, and we give a survey of partial results for a number of other Banach spaces. We then investigate the lattice of closed ideals in ℬ(F), where F is one of Figiel's reflexive Banach spaces not isomorphic to their Cartesian squares. Our main result is that this lattice is uncountable.},
author = {Niels Jakob Laustsen, Richard J. Loy},
journal = {Banach Center Publications},
keywords = {ideal lattice; operator; Banach space; Banach algebra},
language = {eng},
number = {1},
pages = {245-264},
title = {Closed ideals in the Banach algebra of operators on a Banach space},
url = {http://eudml.org/doc/286174},
volume = {67},
year = {2005},
}

TY - JOUR
AU - Niels Jakob Laustsen
AU - Richard J. Loy
TI - Closed ideals in the Banach algebra of operators on a Banach space
JO - Banach Center Publications
PY - 2005
VL - 67
IS - 1
SP - 245
EP - 264
AB - In general, little is known about the lattice of closed ideals in the Banach algebra ℬ(E) of all bounded, linear operators on a Banach space E. We list the (few) Banach spaces for which this lattice is completely understood, and we give a survey of partial results for a number of other Banach spaces. We then investigate the lattice of closed ideals in ℬ(F), where F is one of Figiel's reflexive Banach spaces not isomorphic to their Cartesian squares. Our main result is that this lattice is uncountable.
LA - eng
KW - ideal lattice; operator; Banach space; Banach algebra
UR - http://eudml.org/doc/286174
ER -