Faculty Publications

Codimension 1 Minimal Projections Onto The Lines In LP

Document Type

Article

Keywords

Formulas for minimal projections, Minimal projection, Uniqueness of minimal projections

Journal/Book/Conference Title

Journal of Approximation Theory

Volume

283

Abstract

Let X denote a real Banach space and V a subspace of X; we say that projection Pmin:X→V is minimal if ‖Pmin‖≤‖P‖ for every projection P from X to V. Considered as a subspace of Lebesgue space Lp[−1,1] (p≥1), let Y≔[1,t] denote the subspace of lines. In this paper we consider several natural codimension 1 overspaces X⊃Y (within Lp) and characterize minimal projections Pmin:X→Y for p=2n. The characterization utilizes the (so called) Chalmers–Metcalf operator and as such makes heavy use of extremal pairs associated with projections. We include results that show minimal projections in this setting are unique and include a section where algorithms and numerical results for ‖Pmin‖ are given.

Department

Department of Mathematics

Original Publication Date

11-1-2022

DOI of published version

10.1016/j.jat.2022.105812

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