The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces.

Laustsen, Niels Jakob and Loy, Richard J. and Read, Charles J. (2004) The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces. Journal of Functional Analysis, 214 (1). pp. 106-131. ISSN 0022-1236

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Abstract

Very few Banach spaces E are known for which the lattice of closed ideals in the Banach algebra of all (bounded, linear) operators on E is fully understood. Indeed, up to now the only such Banach spaces are, up to isomorphism, Hilbert spaces and the sequence spaces c0 and ℓp for 1p<∞. We add a new member to this family by showing that there are exactly four closed ideals in for the Banach space E(ℓ2n)c0, that is, E is the c0-direct sum of the finite-dimensional Hilbert spaces ℓ21,ℓ22,…,ℓ2n,… .

Item Type: Journal Article
Journal or Publication Title: Journal of Functional Analysis
Uncontrolled Keywords: /dk/atira/pure/researchoutput/libraryofcongress/qa
Subjects:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 21081
Deposited By: Dr Niels Jakob Laustsen
Deposited On: 11 Dec 2008 10:17
Refereed?: No
Published?: Published
Last Modified: 19 Sep 2019 23:40
URI: https://eprints.lancs.ac.uk/id/eprint/21081

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