A new version of the Hahn-Banach theorem |
| |
Authors: | Email author" target="_blank">S?SimonsEmail author |
| |
Institution: | (1) Department of Mathematics, University of California, 93106-3080 Santa Barbara, CA, USA |
| |
Abstract: | We discuss a new version of the Hahn-Banach theorem,
with applications to linear and nonlinear functional analysis,
convex analysis, and the theory of monotone multifunctions.
We show how our result can be used to prove a localized
version of the Fenchel-Moreau formula - even when the classical
Fenchel-Moreau formula is valid, the proof of it given here avoids
the problem of the vertical hyperplane . We give a short proof of
Rockafellar s fundamental result on dual problems and Lagrangians
- obtaining a necessary and sufficient condition instead of the
more usual sufficient condition. We show how our result leads to
a proof of the (well-known) result that if a monotone multifunction on a
normed space has bounded range then it has full domain. We also show how
our result leads to generalizations of an existence theorem with no
a priori scalar bound that has proved
very useful in the investigation of monotone multifunctions, and show
how the estimates obtained can be applied to Rockafellar s surjectivity
theorem for maximal monotone multifunctions in reflexive Banach spaces.
Finally, we show how our result leads easily to a result on convex functions
that can be used to establish a minimax theorem. |
| |
Keywords: | 46A22 46N10 49J35 47H05 |
本文献已被 SpringerLink 等数据库收录! |
|