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

Niels Jakob Laustsen*, Richard J. Loy, Charles J. Read

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    25 Citations (Scopus)

    Abstract

    Very few Banach spaces E are known for which the lattice of closed ideals in the Banach algebra ℬ (B) 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 1≤p<∞. We add a new member to this family by showing that there are exactly four closed ideals in ℬ (E) for the Banach space E:=(⊕ℓ2n) c0, that is, E is the c0-direct sum of the finite-dimensional Hilbert spaces ℓ2 1,ℓ22,...,ℓ2 n,...

    Original languageEnglish
    Pages (from-to)106-131
    Number of pages26
    JournalJournal of Functional Analysis
    Volume214
    Issue number1
    DOIs
    Publication statusPublished - 1 Sept 2004

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