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Modulus of dentability in $L^{1}+L^{\infty }$

Tom 79 / 2008

Adam Bohonos, Ryszard P/luciennik Banach Center Publications 79 (2008), 39-51 MSC: 46E30, 46B20, 46B42. DOI: 10.4064/bc79-0-2

Streszczenie

We introduce the notion of the modulus of dentability defined for any point of the unit sphere $S( X) $ of a Banach space $X.$ We calculate effectively this modulus for denting points of the unit ball of the classical interpolation space $L^{1}+L^{\infty }.$ Moreover, a criterion for denting points of the unit ball in this space is given. We also show that none of denting points of the unit ball of $L^{1}+L^{\infty }$ is a LUR-point. Consequently, the set of LUR-points of the unit ball of $L^{1}+L^{\infty }$ is empty.

Autorzy

  • Adam BohonosInstitute of Mathematics
    Szczecin University of Technology
    Al. Piastów 48/49
    70-310 Szczecin, Poland
    e-mail
  • Ryszard P/luciennikInstitute of Mathematics
    Poznań University of Technology
    Piotrowo 3A
    60-965 Poznań, Poland
    e-mail

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