Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Quasi-differentiable functions of Banach spaces


Author: Victor Goodman
Journal: Proc. Amer. Math. Soc. 30 (1971), 367-370
MSC: Primary 46.45; Secondary 57.00
MathSciNet review: 0284811
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Nonzero Fréchet differentiable functions with bounded support do not exist on certain real separable Banach spaces. As a result, the class of differentiable functions on such spaces is too small to be useful. For example, the class of differentiable functions on certain spaces does not separate disjoint closed subsets of the space. It is shown that this separation problem does not arise if Fréchet differentiability is replaced by the weaker condition of quasi-differentiability. Furthermore, it is shown that any bounded uniformly continuous function on a real separable Banach space is the uniform limit of quasi-differentiable functions.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46.45, 57.00

Retrieve articles in all journals with MSC: 46.45, 57.00


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0284811-3
PII: S 0002-9939(1971)0284811-3
Keywords: Differentiable functions on Banach spaces, calculus on Banach spaces, smoothing operators
Article copyright: © Copyright 1971 American Mathematical Society