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A short note on hereditary Mazur intersection property

Pradipta Bandyopadhyay, Deepak Gothwal

Abstract

In this note, we prove that hereditary Mazur intersection property (MIP) does not imply Fréchet smoothness using an example by Borwein and Fabian (1993).

A short note on hereditary Mazur intersection property

Abstract

In this note, we prove that hereditary Mazur intersection property (MIP) does not imply Fréchet smoothness using an example by Borwein and Fabian (1993).
Paper Structure (2 sections, 5 theorems, 2 equations)

This paper contains 2 sections, 5 theorems, 2 equations.

Table of Contents

  1. Introduction
  2. Main Results

Key Result

Theorem 2

For a Banach space $(X, \|\cdot\|)$, consider the following statements : Then $(a) \implies (b) \implies (c)$.

Theorems & Definitions (9)

  • Definition 1
  • Theorem 2
  • Theorem 3
  • proof
  • Corollary 4
  • proof
  • Corollary 5
  • Theorem 6
  • proof