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Journal of Convex Analysis 30 (2023), No. 1, 317--328
Copyright Heldermann Verlag 2023

More on Connexions Between Subdifferential and Weak Compactness of Sublevels

Pedro Pérez-Aros
Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins, Rancagua, Chile

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

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.

Keywords: Convex function, conjugate function, inf-convolution, infcompact function, weak compactness, subdifferential, sublevel.

MSC: 46A25, 46A04, 46A50.

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