Local completeness of locally pseudoconvex spaces and Borwein-Preiss variational principle

• Autorzy: J. H. Qiu , S. Rolewicz
• Języki publikacji: EN

Abstrakty

EN

The notion of local completeness is extended to locally pseudoconvex spaces. Then a general version of the Borwein-Preiss variational principle in locally complete locally pseudoconvex spaces is given, where the perturbation is an infinite sum involving differentiable real-valued functions and subadditive functionals. From this, some particular versions of the Borwein-Preiss variational principle are derived. In particular, a version with respect to the Minkowski gauge of a bounded closed convex set in a locally convex space is presented. In locally convex spaces it can be shown that the relevant perturbation only consists of a single summand if and only if the bounded closed convex set has the quasi-weak drop property if and only if it is weakly compact. From this, a new description of reflexive locally convex spaces is obtained.

Kategorie tematyczne

• 49J45: Methods involving semicontinuity and convergence; relaxation
• 46A55: Convex sets in topological linear spaces; Choquet theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 183
• Numer: 2
• Strony: 99-115

Daty

wydano

2007

Twórcy

autor

J. H. Qiu

• Department of Mathematics, Suzhou University, Suzhou, Jiangsu 215006, People's Republic of China

autor

S. Rolewicz

• Institute of Mathematics, Polish Academy of Sciences, P.O. Box 21, Śniadeckich 8, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/sm183-2-1