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Caracterisation of Frechet differentiability norm for dual complex Banach spaces

Mohammad Daher

Abstract

Let X be a complex Banach space, in this work we characterize the property of Frechet differentiability for the dual space of X. In the following, we show that if the dual space of X is Gateaux differentiable, then the dual space of Lp(X) has the same property for all p betwwen one and infiniy

Caracterisation of Frechet differentiability norm for dual complex Banach spaces

Abstract

Let X be a complex Banach space, in this work we characterize the property of Frechet differentiability for the dual space of X. In the following, we show that if the dual space of X is Gateaux differentiable, then the dual space of Lp(X) has the same property for all p betwwen one and infiniy
Paper Structure (1 section, 5 theorems, 15 equations)

This paper contains 1 section, 5 theorems, 15 equations.

Table of Contents

  1. Introduction

Key Result

Theorem 1.5

Let $X$ be a complex Banach space. Then $X^{\ast }$ is uniformly smooth if and only if $X^{\ast }$ satisfies the condition 2).

Theorems & Definitions (9)

  • Definition 1.1
  • Definition 1.2
  • Definition 1.3
  • Definition 1.4
  • Theorem 1.5
  • Corollary 1.6
  • Theorem 1.8
  • Lemma 1.9
  • Lemma 1.10