Bennett-Carl inequalities for symmetric Banach sequence spaces and unitary ideals

1999/04/28 by Andreas Defant, Defant, Andreas, Carsten Michels +1
Mathematics · #47B10 (primary) #47B37 (secondary) #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:47B10 #msc:47B37

paper · pdf · doi:10.48550/arxiv.math/9904157

17 pages

arxiv created 1999/04/28 · openalex publication_date 1999/04/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an abstract interpolation theorem which interpolates the (r,2)-summing and (s,2)-mixing norm of a fixed operator in the image and the range space. Combined with interpolation formulas for spaces of operators we obtain as an application the original Bennett-Carl inequalities for identities acting between Minkowski spaces l_u as well as their analogues for Schatten classes S_u. Furthermore, our techniques motivate a study of Bennett-Carl inequalities within a more general setting of symmetric Banach sequence spaces and unitary ideals.

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• Noncommutative Boyd interpolation theorems
• Sharp interpolation inequalities for discrete operators and applications
• Summing inclusion maps between symmetric sequence spaces
• Interpolation theorems for operators in non-commutative vector-valued symmetric spaces
• Notes on Bernstein spaces, sampling, Boas interpolation formulas and their extensions to Banach spaces