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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The product of a Gâteaux differentiability space and a separable space is a Gâteaux differentiability space


Authors: Lixin Cheng and Marián Fabian
Journal: Proc. Amer. Math. Soc. 129 (2001), 3539-3541
MSC (2000): Primary 46B20, 46G05, 26E15, 58C20
Published electronically: July 2, 2001
MathSciNet review: 1860485
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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.


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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, Žitná 25, 115 67 Prague 1, Czech Republic

DOI: http://dx.doi.org/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
Published electronically: July 2, 2001
Additional Notes: The first author was supported by NSFC 10071063, F00021
The second author was supported by GA ČR 201-98-1449, GA ČR 201/01/1198, and AV 1019003
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2001 American Mathematical Society