On p-Convexity and q-Concavity in Non-Commutative Symmetric Spaces

Peter Dodds, Theresa Dodds, Fyodor Sukochev

    Research output: Contribution to journalArticlepeer-review

    22 Citations (Scopus)

    Abstract

    It is shown that if a symmetric Banach space E on the positive semi-axis is p-convex (q-concave) then so is the corresponding non-commutative symmetric space E(τ) of τ-measurable operators affiliated with some semifinite von Neumann algebra (M, τ), with preservation of the convexity (concavity) constants in the case that M is non-atomic. Similar statements hold in the case that E satisfies an upper (lower) p-estimate and extend to the more general semifinite setting earlier results due to Arazy and Lin for unitary matrix spaces.

    Original languageEnglish
    Pages (from-to)91-114
    Number of pages24
    JournalIntegral Equations and Operator Theory
    Volume78
    Issue number1
    DOIs
    Publication statusPublished - 2014

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