International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 4, Pages 705-713
doi:10.1155/S0161171283000605
Supremum norm differentiability
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.
Abstract
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 ℓ∞(E) of all bounded sequences in E and to the space B(ℓ1,E) of all bounded linear operators from ℓ1 into E