|
Separable determination of integrability and minimality of the Clarke subdifferential mapping
Author(s):
Jonathan
M.
Borwein;
Warren
B.
Moors
Journal:
Proc. Amer. Math. Soc.
128
(2000),
215-221.
MSC (1991):
Primary 49J52, 46N10;
Secondary 58C20
Posted:
September 9, 1999
MathSciNet review:
1622793
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper we show that the study of integrability and  -representability of Lipschitz functions defined on arbitrary Banach spaces reduces to the study of these properties on separable Banach spaces.
References:
- 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
- 9.
- L. Thibault, ``On generalized differentials and subdifferentials of Lipschitz vector-valued functions,'' Nonlinear Anal. 6 (1982), 1037-1053. MR 85e:58020
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
49J52, 46N10,
58C20
Retrieve articles in all Journals with
MSC (1991):
49J52, 46N10,
58C20
Additional Information:
Jonathan
M.
Borwein
Affiliation:
CECM, Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
Email:
jborwein@cecm.sfu.ca
Warren
B.
Moors
Affiliation:
Department of Mathematics, University of Waikato, Private Bag 3105, Hamilton, New Zealand
Email:
moors@math.waikato.ac.nz
DOI:
10.1090/S0002-9939-99-05001-7
PII:
S 0002-9939(99)05001-7
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
Posted:
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
Copyright of article:
Copyright
1999,
American Mathematical Society
|
