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

100%
Laustsen N., Loy R.
Banach Center Publications
|
2005
|
tom 67
|
nr 1
245-264
EN
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.
2
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An amalgamation of the Banach spaces associated with James and Schreier, Part I: Banach-space structure

100%
Bird A., Laustsen N.
Banach Center Publications
|
2010
|
tom 91
|
nr 1
45-76
EN
We create a new family of Banach spaces, the James-Schreier spaces, by amalgamating two important classical Banach spaces: James' quasi-reflexive Banach space on the one hand and Schreier's Banach space giving a counterexample to the Banach-Saks property on the other. We then investigate the properties of these James-Schreier spaces, paying particular attention to how key properties of their 'ancestors' (that is, the James space and the Schreier space) are expressed in them. Our main results include that each James-Schreier space is c₀-saturated and that no James-Schreier space embeds in a Banach space with an unconditional basis.
3
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A properly infinite Banach *-algebra with a non-zero, bounded trace

81%
Dales H., Laustsen N., Read C.
Studia Mathematica
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2003
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tom 155
|
nr 2
107-129
EN
A properly infinite C*-algebra has no non-zero traces. We construct properly infinite Banach *-algebras with non-zero, bounded traces, and show that there are even such algebras which are fairly "close" to the class of C*-algebras, in the sense that they can be hermitian or *-semisimple.
4
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Maximal left ideals of the Banach algebra of bounded operators on a Banach space

71%
Dales H., Kania T., Kochanek T., Koszmider P., Laustsen N.
Studia Mathematica
|
2013
|
tom 218
|
nr 3
245-286
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