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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: Article
    Journal or Publication Title: Journal of Functional Analysis
    Uncontrolled Keywords: Ideal lattice ; operator ; Banach space ; Banach algebra
    Subjects: Q Science > QA Mathematics
    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: 09 Oct 2013 13:14
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/21081

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