International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 3, Pages 433-439
doi:10.1155/S0161171285000473
Essential supremum norm differentiability
1Department of Mathematical Sciences, Northern Illinois University, DeKalb 60115, IL, USA
2Department of Mathematics, University of Saskatchewan, Saskatoon S7N 0W0, SK, Canada
Received 26 April 1985
Copyright © 1985 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 in L∞(μ,X) are obtained, where (Ω,∑,μ) is a finite measure space and X is a real Banach space. An application of these results is given to the space B(L1(μ,ℝ),X) of all bounded linear operators from L1(μ,ℝ) into X.