On coincidence results for summing multilinear operators: interpolation, $$\ell _1$$ℓ1-spaces and cotype

• Autores: Frédéric Bayart , Daniel M. Pellegrino, Pilar Rueda
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 71, Fasc. 2, 2020, págs. 301-318
• Idioma: inglés
• DOI: 10.1007/s13348-019-00261-6
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• Resumen

  • Grothendieck’s theorem asserts that every continuous linear operator from ℓ1 to ℓ2 is absolutely (1, 1)-summing. This kind of result is commonly called coincidence result. In this paper we investigate coincidence results in the multilinear setting, showing how the cotype of the spaces involved affect such results. The special role played by ℓ1 spaces is also investigated with relation to interpolation of tensor products. In particular, an open problem on the interpolation of m injective tensor products is solved.

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