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The product of a Gâteaux differentiability space and a separable space is a Gâteaux differentiability space
Author(s):
Lixin
Cheng;
Marián
Fabian
Journal:
Proc. Amer. Math. Soc.
129
(2001),
3539-3541.
MSC (2000):
Primary 46B20, 46G05, 26E15, 58C20
Posted:
July 2, 2001
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Abstract:
This paper shows that the product of a Gâteaux differentiability space and a separable Banach space is again a Gâteaux differentiability space.
References:
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- [A]
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- M. J. Fabian, Gâteaux differentiability of convex functions and topology. Weak Asplund spaces, J. Wiley & Sons, Interscience, New York, 1997. MR 98h:46009
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- J. R. Giles, Convex analysis with application in differentiation of convex functions, Research Notes in Math., No. 58, Pitman, Boston-London-Melbourne, 1982. MR 83g:46001
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- R. R. Phelps, Convex functions, monotone operators, and differentiability, Lecture Notes in Math., No. 1364, Springer Verlag, 1989; 2nd Edition, 1993. MR 90g:46063; MR 94f:46055
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Additional Information:
Lixin
Cheng
Affiliation:
Department of Mathematics, Xiamen University, Xiamen 361005, People's Republic of China
Marián
Fabian
Affiliation:
Mathematical Institute, Czech Academy of Sciences, Zitná 25, 115 67 Prague 1, Czech Republic
DOI:
10.1090/S0002-9939-01-06252-9
PII:
S 0002-9939(01)06252-9
Keywords:
Convex function,
Banach space,
G\^ateaux differentiability space
Received by editor(s):
March 16, 2000
Posted:
July 2, 2001
Additional Notes:
The first author was supported by NSFC 10071063, F00021
The second author was supported by GA CR 201-98-1449, GA CR 201/01/1198, and AV 1019003
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2001,
American Mathematical Society
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