A+ CATEGORY SCIENTIFIC UNIT

Equivalences involving $(p,q)$-multi-norms

Volume 225 / 2014

Oscar Blasco, H. G. Dales, Hung Le Pham Studia Mathematica 225 (2014), 29-59 MSC: Primary 46B15; Secondary 46B28, 46B42, 47L10. DOI: 10.4064/sm225-1-3

Abstract

We consider $(p,q)$-multi-norms and standard $t$-multi-norms based on Banach spaces of the form $L^r(\varOmega )$, and resolve some question about the mutual equivalence of two such multi-norms. We introduce a new multi-norm, called the $[p,q]$-concave multi-norm, and relate it to the standard $t$-multi-norm.

Authors

  • Oscar BlascoDepartamento de Análisis Matemático
    Universidad de Valencia
    46100 Burjassot, Valencia, Spain
    e-mail
  • H. G. DalesDepartment of Mathematics and Statistics
    University of Lancaster
    Lancaster LA1 4YF, United Kingdom
    e-mail
  • Hung Le PhamSchool of Mathematics, Statistics
    and Operations Research
    Victoria University of Wellington
    Wellington 6140, New Zealand
    e-mail

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