Nonsquareness and Locally Uniform Nonsquareness in Orlicz-Bochner Function Spaces Endowed with Luxemburg Norm

Shaoqiang Shang,Yongqiang Fu,Yunan Cui

doi:10.1155/2011/875649

Abstract

Criteria for nonsquareness and locally uniform nonsquareness of Orlicz-Bochner function spaces equipped with Luxemburg norm are given. We also prove that, in Orlicz-Bochner function spaces generated by locally uniform nonsquare Banach space, nonsquareness and locally uniform nonsquareness are equivalent.

Highlights

A lot of nonsquareness concepts in Banach spaces are known see 1
One of reasons is that these properties are strongly related to the fixed point property see 2
Because of the complicated structure of Orlicz-Bochner function spaces equipped with the Luxemburg norm, the criteria for nonsquareness and locally uniform nonsquareness of them have not been found yet

Summary

Introduction

A lot of nonsquareness concepts in Banach spaces are known see 1. The criteria for nonsquareness and locally uniform nonsquareness in the classical Orlicz function spaces have been given in 3, 4 already. The aim of this paper is to give criteria for nonsquareness and locally uniform nonsquareness of Orlicz-Bochner function spaces equipped with Luxemburg norm.

Objectives

Results

Conclusion