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Ideals of multilinear mappings via Orlicz spaces and translation invariant operators

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  • Mieczysław Mastyło
  • Enrique A. Sánchez Pérez

Abstract

We study some new summability properties of multilinear operators. We introduce the concepts of φ‐summing, φ semi‐integral and φ‐dominated multilinear maps generated by Orlicz functions. We prove a variant of Pietsch's domination theorem for φ‐summing operators, providing also a characterization of φ‐dominated operators in terms of factorizations. We analyze vector‐valued inequalities associated to these maps, which are applied to obtain general variants of multiple summing operators. We also study translation invariant multilinear operators acting in products of spaces of continuous functions, proving that a factorization theorem can be obtained for them as a consequence of a suitable representation of the corresponding normalized Haar measure.

Suggested Citation

  • Mieczysław Mastyło & Enrique A. Sánchez Pérez, 2021. "Ideals of multilinear mappings via Orlicz spaces and translation invariant operators," Mathematische Nachrichten, Wiley Blackwell, vol. 294(5), pages 956-976, May.
    • Handle: RePEc:bla:mathna:v:294:y:2021:i:5:p:956-976
    DOI: 10.1002/mana.201900380
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