On the pointwise maximum of convex functions
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- by S. P. Fitzpatrick and S. Simons PDF
- Proc. Amer. Math. Soc. 128 (2000), 3553-3561 Request permission
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
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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
- MR Author ID: 189831
- Email: simons@math.ucsb.edu
- Received by editor(s): May 11, 1998
- Received by editor(s) in revised form: January 29, 1999
- Published electronically: May 18, 2000
- Communicated by: Dale Alspach
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3553-3561
- MSC (2000): Primary 46N10, 49J52, 49N15
- DOI: https://doi.org/10.1090/S0002-9939-00-05449-6
- MathSciNet review: 1690986
Dedicated: This paper is dedicated to Professor Robert Phelps