Convex functions on dual Orlicz spaces View Full Text


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Article Info

DATE

2019-02-07

AUTHORS

Freddy Delbaen, Keita Owari

ABSTRACT

In the dual LΦ∗ of a Δ2-Orlicz space LΦ, that we call a dual Orlicz space, we show that a proper (resp. finite) convex function is lower semicontinuous (resp. continuous) for the Mackey topology τ(LΦ∗,LΦ) if and only if on each order interval [-ζ,ζ]={ξ:-ζ≤ξ≤ζ} (ζ∈LΦ∗), it is lower semicontinuous (resp. continuous) for the topology of convergence in probability. For this purpose, we provide the following Komlós type result: every norm bounded sequence (ξn)n in LΦ∗ admits a sequence of forward convex combinations ξ¯n∈conv(ξn,ξn+1,…) such that supn|ξ¯n|∈LΦ∗ and ξ¯n converges a.s. More... »

PAGES

1-14

References to SciGraph publications

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  • Journal

    TITLE

    Positivity

    ISSUE

    N/A

    VOLUME

    N/A

    From Grant

  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11117-019-00651-x

    DOI

    http://dx.doi.org/10.1007/s11117-019-00651-x

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1111982779


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