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

By Niels Jakob Laustsen, Richard J. Loy and Charles J. Read

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,…

Year: 2004
OAI identifier: oai:eprints.lancs.ac.uk:21081
Provided by: Lancaster E-Prints

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