Abstract:
Characterizations of properties of operators in a Banach space setting have been
done over many years with interesting results obtained. Dentability of sets and
norm-attainable mappings is one of the important properties that have been
considered. Most researchers have worked on dentable sets with regard to density
of norm-attainable operators. We characterize dentable sets and mappings. This
work establishes a link between measure theory, norm-attainability and dentability
with the help of Radon-Nikodým Property. It also improves the understanding of
optimization problems at a deeper level.
