Supremum norm differentiability

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

Keywords

• Banach space
• continuos functions
• vector-valued functions
• supremum norm
• smooth points.