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

J. H. Qiu, and S. Rolewicz. "Local completeness of locally pseudoconvex spaces and Borwein-Preiss variational principle." Studia Mathematica 183.2 (2007): 99-115. <http://eudml.org/doc/285354>.

@article{J2007,
abstract = {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.},
author = {J. H. Qiu, S. Rolewicz},
journal = {Studia Mathematica},
keywords = {locally pseudoconvex space; variational principle; quasi-weak drop property; weakly compact set; reflexivity},
language = {eng},
number = {2},
pages = {99-115},
title = {Local completeness of locally pseudoconvex spaces and Borwein-Preiss variational principle},
url = {http://eudml.org/doc/285354},
volume = {183},
year = {2007},
}

TY - JOUR
AU - J. H. Qiu
AU - S. Rolewicz
TI - Local completeness of locally pseudoconvex spaces and Borwein-Preiss variational principle
JO - Studia Mathematica
PY - 2007
VL - 183
IS - 2
SP - 99
EP - 115
AB - 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.
LA - eng
KW - locally pseudoconvex space; variational principle; quasi-weak drop property; weakly compact set; reflexivity
UR - http://eudml.org/doc/285354
ER -