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Separable determination
of integrability and minimality
of the Clarke subdifferential mapping

Authors: Jonathan M. Borwein and Warren B. Moors
Journal: Proc. Amer. Math. Soc. 128 (2000), 215-221
MSC (1991): Primary 49J52, 46N10; Secondary 58C20
Published electronically: September 9, 1999
MathSciNet review: 1622793
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we show that the study of integrability and $D$-representability of Lipschitz functions defined on arbitrary Banach spaces reduces to the study of these properties on separable Banach spaces.

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

  • 1. J. M. Borwein, ``Minimal cuscos and subgradients of Lipschitz functions,'' in Fixed Point Theory and Its Applications, (J. B. Baillion and M. Thera, Eds.), Pitman Lecture Notes in Math., pp. 57-82, Longman, Essex, UK, 1991. MR 92j:46077
  • 2. J. M. Borwein and W. B. Moors, ``Essentially smooth Lipschitz functions,'' J. Funct. Anal. 149 (1997), 305-351. MR 98i:58028
  • 3. J. M. Borwein and W. B. Moors, ``Null sets and essentially smooth Lipschitz functions,'' SIAM J. Optim. 8 (1998), 309-323. CMP 98:11
  • 4. J. M. Borwein and W. B. Moors, ``Lipschitz functions with minimal Clarke subdifferential mappings,'' Proc. Optim. Mininconference III: The Uni. Melbourne, July 18 1996; eds. B. M. Glover, B. D. Craven and D. Ralph, Ballarat, Vic. Uni. Ballarat (1997), 5-12.
  • 5. J. M. Borwein, W. B. Moors and Xianfu Wang, ``Generalized subdifferentials: a Baire categorical approach,'' Compte. Rendu. Roy. Soc. Canada to appear.
  • 6. J. P. R. Christensen,``On sets of Haar measure zero in Abelian groups,'' Israel J. Math. 13 (1972), 255-260. MR 48:4637
  • 7. F. H. Clarke, Optimization and Nonsmooth Analysis, John Wiley, New York (1971).
  • 8. W. B. Moors, ``A characterisation of minimal subdifferential mappings of locally Lipschitz functions,'' Set-Valued Analysis 3 (1995), 129-141. MR 96e:58013
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Additional Information

Jonathan M. Borwein
Affiliation: CECM, Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6

Warren B. Moors
Affiliation: Department of Mathematics, University of Waikato, Private Bag 3105, Hamilton, New Zealand

Keywords: Separable reduction, integrability, $D$-representability, minimal cusco.
Received by editor(s): October 22, 1997
Received by editor(s) in revised form: March 18, 1998
Published electronically: September 9, 1999
Additional Notes: The first author’s research was supported by NSERC and the Shrum Endowment at Simon Fraser University.
Communicated by: Dale Alspach
Article copyright: © Copyright 1999 American Mathematical Society

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