Small Transitive Families of Dense Operator Ranges

William Longstaff

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)


    In complex, separable, infinite-dimensional Hilbert space there exist 5 proper dense operator ranges with the property that every operator leaving each of them invariant is a scalar multiple of the identity. The algebra of operators leaving a pair of proper dense operator ranges invariant can have an infinite nest of invariant subspaces. A slight extension of Foias' Theorem shows that it can also have a non-trivial reducing subspace.
    Original languageEnglish
    Pages (from-to)343-350
    JournalIntegral Equations and Operator Theory
    Issue number3
    Publication statusPublished - 2003


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