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

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<mark>Journal publication date</mark>1/09/2004
<mark>Journal</mark>Journal of Functional Analysis
Issue number1
Volume214
Number of pages26
Pages (from-to)106-131
<mark>State</mark>Published
<mark>Original language</mark>English

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,… .