Stability constants and the homology of quasi-Banach spaces

2013/07/16 by Jesús M. F. Castillo, Castillo, Jesús M. F., Félix Cabello Sánchez +1
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results

paper · pdf · doi:10.48550/arxiv.1307.4382

openalex publication_date 2013/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We affirmatively solve the main problems posed by Laczkovich and Paulin in Stability constants in linear spaces, Constructive Approximation 34 (2011) 89--106 (do there exist cases in which the second Whitney constant is finite while the approximation constant is infinite?) and by Cabello and Castillo in The long homology sequence for quasi-Banach spaces, with applications, Positivity 8 (2004) 379--394 (do there exist Banach spaces X,Y for which \Ext(X,Y) is Hausdorff and non-zero?). In fact, we show that these two problems are the same.

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