Abstract
Our goal in this paper is to prove versions of the Hahn—Banach and Banach—Steinhaus theorems for convex processes. For the first theorem, we prove that each real convex process corresponds to a sublinear or superlinear functional and then we extend these. For the second theorem, we previously show that there is a seminorm naturally associated to the class of lower semi-continuous convex processes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J.-P. Aubin andI. Ekeland,Applied nonlinear analysis, Wiley Interscience, New York, 1984.MR 87a: 58002
R. T. Rockafellar,Convex analysis, Princeton University Press, Princeton, 1970.MR 43: 445
R. T. Rockafellar,Monotone processes of convex and concave type, American Math. Society, Providence, 1967.MR 37: 825
W. Rudin,Functional analysis, McGraw-Hill, New York, 1973.MR 51: 1315
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Abreu, J., Etcheberry, A. Hahn—Banach and Banach—Steinhaus theorems for convex processes. Period Math Hung 20, 289–297 (1989). https://doi.org/10.1007/BF01848992
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01848992