Faculty Publications

Simultaneous Minimal Extensions with Applications

Document Type

Article

Keywords

minimal extensions, Minimal projections

Journal/Book/Conference Title

Real Analysis Exchange

Volume

50

Issue

1

First Page

159

Last Page

177

Abstract

When X denotes a (real) Banach space and V a subspace of X, we say that projection Po: X → V is minimal if ∥Po∥ ≼ ∥P∥ for every projection P from X to V. We take a view on minimal projections as minimal extensions of operators and consider generalizations of the Hahn–Banach Theorem, such as the simultaneous extension of operators. We provide several applications using polynomial subspaces of the Lebesgue space L4[−1,1] and project these subspaces onto V = [1,t], the subspace of lines. We obtain new numerical results in this direction.

Department

Department of Mathematics

Original Publication Date

5-8-2025

DOI of published version

10.14321/realanalexch.1721734662

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