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The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces |
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| Authors: | Niels Jakob Laustsen Richard J Loy |
| Affiliation: | a Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark b Mathematical Sciences Institute, Australian National University, Canberra ACT 0200, Australia c Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, UK |
| 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 ?p for 1?p<∞. We add a new member to this family by showing that there are exactly four closed ideals in  for the Banach space E?(⊕?2n)c0, that is, E is the c0-direct sum of the finite-dimensional Hilbert spaces ?21,?22,…,?2n,… . |
| Keywords: | primary 47L10 46H10 secondary 47L20 46B45 |
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