Faculty Publications

Title

On the difficulty of preserving monotonicity via projections and related results

Document Type

Article

Keywords

Monotonicity, Projections, Shape-preservation

Journal/Book/Conference Title

Jaen Journal on Approximation

Volume

2

Issue

1

First Page

1

Last Page

12

Abstract

A subspace V of a Banach space X is said to be complemented if there exists a (bounded) projection mapping X onto V. Obviously all subspaces of finitedimension are complemented. The goal of this note is to show that there are (relatively) few monotonically complemented subspaces of finite-dimension in X =(C[a, b], Y Y∞); that is, finite-dimensional subspaces V ⊂ X for which there exists a projection P: X → V such that Pf is monotone-increasing whenever f is. We obtain several corollaries from this consideration, including a result describing the difficulty of preserving n-convexity via a projection. © 2010 Universidad de Jaén.

Original Publication Date

6-21-2010

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