Download On the Moreau-Rockafellar-Robinson condition in Banach spaces

Speaker: Michel Thera
Title: On the Moreau-Rockafellar-Robinson condition in Banach spaces
As well known, the Moreau-Rockafellar-Robinson internal point qualification condition
is sufficient to ensure that the infimal convolution of the conjugates of two extendedreal-valued convex lower semi-continuous functions defined on a locally convex
space is exact, and that the sub-differential of the sum of these functions is the
sum of their sub-differentials.
During this presentation, which will summarize a recent joint work with Emil Ernst, we
intend to show that this condition is, in a certain sense, also necessary, provided
the underlying space is a Banach space.
The main result is based upon the existence of a non-supporting weak$^\star$ closed hyperplane to any weak$^\star$- closed and convex unbounded linearly
bounded subset of the topological dual of a Banach space.