Continuous selections and reflexive Banach spaces

Gutev, Valentin; Nedev, Stoyan

doi:10.1090/S0002-9939-00-05740-3

Continuous selections and reflexive Banach spaces
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by Valentin Gutev and Stoyan Nedev PDF

Proc. Amer. Math. Soc. 129 (2001), 1853-1860 Request permission

Abstract:

Every l.s.c. mapping $\Phi$ from a space $X$ into the non-empty closed convex subsets of a reflexive Banach space $Y$ admits a continuous selection provided it satisfies a “weak” u.s.c. condition. This result partially generalizes some known selection theorems. Also, it is successful in solving a problem concerning the set of proper lower semi-continuous convex functions on a reflexive Banach space.

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