On differentiability of convex operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:402

Article

Vesely, Libor¹  Zajicek, Ludek² 

[1] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy

[2] Charles Univ Prague, Fac Math & Phys, Prague 18675 8, Czech Republic

关键词: Ordered normed spaces;    Banach lattices;    Convex operators;    Frechet differentiability;    Gateaux differentiability;   

DOI  :  10.1016/j.jmaa.2012.12.073

来源: Elsevier

【 摘 要 】

The main known results on differentiability of continuous convex operators f from a Banach space X to an ordered Banach space Y are due to J.M. Borwein and N.K. Kirov. Our aim is to prove some supergeneric results, i.e., to show that, sometimes, the set of Gateaux or Frechet nondifferentiability points is not only a first-category set, but also smaller in a stronger sense. For example, we prove that if Y is countably Daniell and the space L(X, Y) of bounded linear operators is separable, then each continuous convex operator f:X -> Y is Frechet differentiable except for a Gamma-null angle-small set. Some applications of such supergeneric results are shown. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free