On isometric stability of complemented subspaces of L_p

1997/09/11 by Beata Randrianantoanina, Randrianantoanina, Beata
Engineering · Mathematics · #46B20 #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.math/9709214

openalex publication_date 1997/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that Rudin-Plotkin isometry extension theorem in L_p implies that when X and Y are isometric subspaces of L_p and p is not an even integer, 1 ≤ p < ∞, then X is complemented in L_p if and only if Y is; moreover the constants of complementation of X and Y are equal. We provide examples demonstrating that this fact fails when p is an even integer larger than 2.

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