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

Houcine Benabdellah¹ ; My Hachem Lalaoui Rhali¹

¹ Department of Mathematics University Cadi Ayyad Faculty of Sciences Semlalia P.O. Box 2390, Marrakesh, Morocco

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 1, pp. 9-18

Résumé

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) $.

Détail

DOI : 10.4064/ba52-1-2

Keywords: study strongly exposed points general bochner banach spaces first characterization strongly exposed points set x selections measurable multifunction mit gamma apply result study strongly exposed points closed unit ball precisely element strongly exposed point strongly exposed point omega omega strongly exposed point mu almost omega