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Composition results for strongly summing and dominated multilinear operators

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Central European Journal of Mathematics

Abstract

In this paper we prove some composition results for strongly summing and dominated operators. As an application we give necessary and sufficient conditions for a multilinear tensor product of multilinear operators to be strongly summing or dominated. Moreover, we show the failure of some possible n-linear versions of Grothendieck’s composition theorem in the case n ≥ 2 and give a new example of a 1-dominated, hence strongly 1-summing bilinear operator which is not weakly compact.

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Authors and Affiliations

  1. Department of Mathematics, Ovidius University of Constanta, Bd. Mamaia 124, 900527, Constanta, Romania

    Dumitru Popa

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  1. Dumitru Popa
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Popa, D. Composition results for strongly summing and dominated multilinear operators. centr.eur.j.math. 12, 1433–1446 (2014). https://doi.org/10.2478/s11533-014-0423-0

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  • DOI: https://doi.org/10.2478/s11533-014-0423-0

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