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Convexity in the interpolation spaces

2022/11/07 by Mohammad Daher, Mohammad, Daher
Mathematics · #46B70 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2211.03441

openalex publication_date 2022/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we study if the norms rotund, uniformly rotund, weakly uniformly rotund, locally uniformly rotund or weakly locally uniformly rotund interpolate in the complex or the real interpolation spaces. We will see that the properties uniformly rotund and weakly uniformly rotund interpolate, but the properties locally uniformly rotund or weakly locally uniformly rotund do not interpolate in general except for the dual interpolation couple.

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