We study the multilinear generalizations of mid p-summing operators using p-dominated operators. We introduce the class of absolutely mid \((p_1,\dots ,p_m)\) -summing multilinear operators and explore this Banach multi-ideal through the theory of tensor products. We obtain a tensor norm of order \(m+1\) associated to this class of multilinear operators. Furthermore, we investigate the class of weakly mid p-dominated multilinear operators, proving a Pietsch Domination-type result for these operators. Consequently, we establish the inclusion relation between weakly mid p-dominated operators.

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On Multilinear Extensions of Mid p-Summing Operators

  • Deepika Baweja,
  • Aleena Philip

摘要

We study the multilinear generalizations of mid p-summing operators using p-dominated operators. We introduce the class of absolutely mid \((p_1,\dots ,p_m)\) -summing multilinear operators and explore this Banach multi-ideal through the theory of tensor products. We obtain a tensor norm of order \(m+1\) associated to this class of multilinear operators. Furthermore, we investigate the class of weakly mid p-dominated multilinear operators, proving a Pietsch Domination-type result for these operators. Consequently, we establish the inclusion relation between weakly mid p-dominated operators.