Proximinality in generalized direct sums

Darapaneni Narayana,T S S R K Rao

doi:10.1155/s0161171204401057

Abstract

We consider proximinality and transitivity of proximinality for subspaces of finite codimension in generalized direct sums of Banach spaces. We give several examples of Banach spaces where proximinality is transitive among subspaces of finite codimension.

Highlights

Let X be a Banach space and let Y be a closed subspace of X
In the first part of the paper, we study proximinal subspaces of finite codimension in generalized direct sums of Banach spaces
Our motivation comes from some recent work of Indumathi [4] where she considered these questions for c0-direct sums of a family of Banach spaces and proved the following

Summary

Introduction

Let X be a Banach space and let Y be a closed subspace of X. In the first part of the paper, we study proximinal subspaces of finite codimension in generalized direct sums of Banach spaces (a concept due to Veselý [9], see below for the definition). We consider transitivity of proximinality among subspaces of finite codimension in c0-direct sums. We give several new examples of spaces where transitivity of proximinality holds among subspaces of finite codimension answering [3, Question 2] in the affirmative.

Results

Conclusion