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Characterization of strongly exposed points in general Kothe-Bochner Banach spaces

Benabdellah H., Lalaoui Rhali M. H.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 1

9-18

We study strongly exposed points in general Kothe-Bochner Banach spaces X(E). We first give a characterization of strongly exposed points of the set of X-selections of a measurable multifunction [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 [my]-almost all [omega is an element of S(f)].