International Journal of Mathematics and Mathematical Sciences 
Volume 6 (1983), Issue 4, Pages 705-713
doi:10.1155/S0161171283000605

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

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