Characterization of Strongly Exposed Points in General Köthe–Bochner Banach Spaces

Volume 52 / 2004

Houcine Benabdellah, My Hachem Lalaoui Rhali Bulletin Polish Acad. Sci. Math. 52 (2004), 9-18 MSC: Primary 05C38, 15A15; Secondary 05A15, 15A18. DOI: 10.4064/ba52-1-2

Abstract

We study strongly exposed points in general Köthe–Bochner Banach spaces $X(E)$. We first give a characterization of strongly exposed points of the set of $X$-selections of a measurable multifunction ${\mit\Gamma}$. We then apply this result to the study of strongly exposed points of the closed unit ball of $X(E)$. Precisely we show that if an element $f$ is a strongly exposed point of $B_{X( E) }$, then $| f| $ is a strongly exposed point of $B_{X}$ and $f( \omega) /\| f( \omega) \| $ is a strongly exposed point of $B_{E}$ for $\mu$-almost all $\omega\in S( f) $.

Authors

  • Houcine BenabdellahDepartment of Mathematics
    University Cadi Ayyad
    Faculty of Sciences Semlalia
    P.O. Box 2390, Marrakesh, Morocco
    e-mail
  • My Hachem Lalaoui RhaliDepartment of Mathematics
    University Cadi Ayyad
    Faculty of Sciences Semlalia
    P.O. Box 2390, Marrakesh, Morocco
    e-mail

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