On positive Cohen weakly nuclear multilinear operators

  • A. Bougoutaia Laghouat University, 03000, Laghouat, Algeria
  • A. Belacel Laghouat University, 03000, Laghouat, Algeria
  • R. Macedo Federal University of Paraíba, 58.051-900, João Pessoa, Brazil
  • H. Hamdi Laghouat University, 03000, Laghouat, Algeria
Keywords: Banach lattice, Pietsch domination theorem, positive $p$-summing operator, tensor norm
Published online: 2023-11-14

Abstract


In this article, we establish new relationships involving the class of Cohen positive strongly $p$-summing multilinear operators. Furthermore, we introduce a new class of multilinear operators on Banach lattices, called positive Cohen weakly nuclear multilinear operators. We establish a Pietsch domination-type theorem for this new class of multilinear operators. As an application, we show that every positive Cohen weakly $p$-nuclear multilinear operator is positive Dimant strongly $p$-summing and Cohen positive strongly $p$-summing. We conclude with a tensor representation of our class.

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How to Cite
(1)
Bougoutaia A., Belacel A., Macedo R., Hamdi H. On Positive Cohen Weakly Nuclear Multilinear Operators. Carpathian Math. Publ. 2023, 15 (2), 396-410.