Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the pointwise maximum of convex functions


Authors: S. P. Fitzpatrick and S. Simons
Journal: Proc. Amer. Math. Soc. 128 (2000), 3553-3561
MSC (2000): Primary 46N10, 49J52, 49N15
Published electronically: May 18, 2000
MathSciNet review: 1690986
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the conjugate of the maximum, $f \vee g$, of $f$ and $g$ when $f$ and $g$ are proper convex lower semicontinuous functions on a Banach space $E$. We show that $(f \vee g)^{**} = f^{**} \vee g^{**}$ on the bidual, $E^{**}$, of $E$ provided that $f$and $g$ satisfy the Attouch-Brézis constraint qualification, and we also derive formulae for $(f \vee g)^{*}$ and for the ``preconjugate'' of $f^{*}\vee g^{*}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46N10, 49J52, 49N15

Retrieve articles in all journals with MSC (2000): 46N10, 49J52, 49N15


Additional Information

S. P. Fitzpatrick
Affiliation: Department of Mathematics and Statistics, University of Western Australia, Nedlands 6907, Australia
Email: fitzpatr@maths.uwa.edu.au

S. Simons
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106-3080
Email: simons@math.ucsb.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05449-6
PII: S 0002-9939(00)05449-6
Keywords: Banach space, convex function, conjugate, biconjugate, maximum, Attouch-Br\'{e}zis constraint qualification, preconjugate
Received by editor(s): May 11, 1998
Received by editor(s) in revised form: January 29, 1999
Published electronically: May 18, 2000
Dedicated: This paper is dedicated to Professor Robert Phelps
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society