12,000

We have over 12,000 students, from over 100 countries, within one of the safest campuses in the UK

93%

93% of Lancaster students go into work or further study within six months of graduating

Home > Research > Publications & Outputs > The lattice of closed ideals in the Banach alge...
View graph of relations

« Back

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

Research output: Contribution to journalJournal article

Published

Journal publication date1/09/2004
JournalJournal of Functional Analysis
Journal number1
Volume214
Number of pages26
Pages106-131
Original languageEnglish

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,… .