Abstract
A selection theorem concerning support points of convex sets in a Banach space is proved. As a corollary we obtain the following result. Denote by BCC (X) the metric space of all nonempty bounded closed convex sets in a Banach space X. Then there exists a continuous mapping S from BCC (X) to X such that S(K) is a support point of K for each K in BCC (X). Moreover, it is possible to prescribe the values of S on a closed discrete subset of BCC(X).
Lingua originale | English |
---|---|
pagine (da-a) | 369-378 |
Numero di pagine | 10 |
Rivista | Archiv der Mathematik |
Volume | 93 |
DOI | |
Stato di pubblicazione | Pubblicato - 2009 |
Keywords
- Bishop-Phelps theorem
- Convex set
- Mathematics (all)
- Selection
- Support functional
- Support point