International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 4, Pages 705-713

Supremum norm differentiability

I. E. Leonard and K. F. Taylor

Department of Mathematics, University of Saskatchewan, Saskatoon S7N 0W0, Saskatchewan, Canada

Received 1 June 1982

Copyright © 1983 I. E. Leonard and K. F. Taylor. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The points of Gateaux and Fréchet differentiability of the norm in C(T,E) are obtained, where T is a locally compact Hausdorff space and E is a real Banach space. Applications of these results are given to the space (E) of all bounded sequences in E and to the space B(1,E) of all bounded linear operators from 1 into E