On The Difficulty Of Preserving Monotonicity Via Projections And Related Results

Authors

Douglas Mupasiri, University of Northern IowaFollow
Michael P. Prophet, University of Northern IowaFollow

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 finite dimension 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 vi A A projection. © 2010 Universidad de Jaén.

Department

Department of Mathematics

Original Publication Date

6-21-2010

Recommended Citation

Mupasiri, Douglas and Prophet, Michael P., "On The Difficulty Of Preserving Monotonicity Via Projections And Related Results" (2010). Faculty Publications. 2085.
https://scholarworks.uni.edu/facpub/2085