Characterization of Strongly Exposed Points in General Köthe–Bochner Banach Spaces
Volume 52 / 2004
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) $.
