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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Official URL: http://dx.doi.org/10.1016/j.jfa.2004.02.009

## 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 |
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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: | 13 Jan 2016 11:12 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/21081 |

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