Norm Derivatives on Spaces of Operators.

摘要: We say the norm is Frechet differentiable at x if convergence to limit in (1.1) uniform for all y~X. Norm derivatives of spaces: LP(dy), 1 ~ p N oo, and C(X) space real continuous functions on a compact Hausdorff X have been studied extensively, see example page 171 [5]. Also necessary sufficient conditions existence these an arbitrary Banach established terms support functionals dual X*, [2]. In this paper we investigate spaces operators % separable Hilbert whose will be defined following section. also give Gateaux derivative B(H): bounded operators, H, with norm. Whenever exists write formula it. are important approximation theory geometry spaces. make use basic theorem Corollary 3.3. See [5], ex. 3.57.