Abstract

We show how our previous paper "Weak compactness of sublevel sets in complete locally convex spaces" [J. Convex Analysis 26/3 (2019) 739--751] allows to derive with quite direct arguments a large number of recent results established in Banach spaces for connexions between subdifferential and weak compactness of sublevel sets. In fact, the arguments extend the results to locally convex spaces.

Author information

Contact details are reproduced from the original publication and may be historical.

Pedro Pérez-Aros

Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins, Rancagua, Chile

pedro.perez@uoh.cl

Lionel Thibault

Institut Montpelliérain A. Grothendieck, Université de Montpellier, France
and: Centro de Modelamiento Matematico, Universidad de Chile, Santiago, Chile

lionel.thibault@umontpellier.fr

Keywords

  • Convex function
  • conjugate function
  • inf-convolution
  • infcompact function
  • weak compactness
  • subdifferential
  • sublevel

Mathematics Subject Classification

46A25, 46A04, 46A50

Suggested citation

P. Pérez-Aros, L. Thibault. “More on Connexions Between Subdifferential and Weak Compactness of Sublevels.” Journal of Convex Analysis 30 (2023), No. 1, 317–328.

Copyright Heldermann Verlag 2023