Convex composite functions in Banach spaces and the primal lowernice property
Authors:
C. Combari, A. Elhilali Alaoui, A. Levy, R. Poliquin and L. Thibault
Journal:
Proc. Amer. Math. Soc. 126 (1998), 37013708
MSC (1991):
Primary 58C20; Secondary 49J52
MathSciNet review:
1451793
Fulltext PDF Free Access
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Abstract: Primal lowernice functions defined on Hilbert spaces provide examples of functions that are ``integrable'' (i.e. of functions that are determined up to an additive constant by their subgradients). The class of primal lowernice functions contains all convex and lower functions. In finite dimensions the class of primal lowernice functions also contains the composition of a convex function with a mapping under a constraint qualification. In Banach spaces certain convex composite functions were known to be primal lowernice (e.g. a convex function had to be continuous relative to its domain). In this paper we weaken the assumptions and provide new examples of convex composite functions defined on a Banach space with the primal lowernice property. One consequence of our results is the identification of new examples of integrable functions on Hilbert spaces.
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Additional Information
C. Combari
Affiliation:
Université de Montpellier II, Laboratoire Analyse Convexe, Place Eugene Bataillon, 34095 Montpellier Cedex 5, France
A. Elhilali Alaoui
Affiliation:
Université de Montpellier II, Laboratoire Analyse Convexe, Place Eugene Bataillon, 34095 Montpellier Cedex 5, France
Address at time of publication:
Falculté des Sciences et Techniques de Marrakech, Université Cadi Ayad, B.P. 618, Marrakech, Maroc
A. Levy
Affiliation:
Department of Mathematics, Bowdoin College, Brunswick, Maine 04011
Email:
alevy@bowdoin.edu
R. Poliquin
Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email:
rene.poliquin@ualberta.ca
L. Thibault
Affiliation:
Université de Montpellier II, Laboratoire Analyse Convexe, Place Eugene Bataillon, 34095 Montpellier Cedex 5, France
DOI:
http://dx.doi.org/10.1090/S000299399804324X
PII:
S 00029939(98)04324X
Keywords:
Primal lowernice functions,
subdifferential,
convex composite functions,
integrable functions
Received by editor(s):
February 16, 1996
Received by editor(s) in revised form:
November 27, 1996
Additional Notes:
The research of R. Poliquin was supported in part by the Natural Sciences and Engineering Research Council of Canada under grant OGP41983.
Communicated by:
Dale Alspach
Article copyright:
© Copyright 1998
American Mathematical Society
