On coincidence results for summing multilinear operators: interpolation, l1-spaces and cotype

被引：0

作者：

Bayart, Frederic ^{[1
]}

Pellegrino, Daniel ^{[2
]}

Rueda, Pilar ^{[3
]}

机构：

[1] Univ Clermont Auvergne, Lab Math Blaise Pascal, Campus Cezeaux 3,Pl Vasarely TSA 60026 CS 60026, F-63178 Aubiere, France

[2] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba, Brazil

[3] Univ Valencia, Fac Matemat, Dept Anal Matemat, C Dr Moliner 50, E-46100 Valencia, Pb Coubtry, Spain

来源：

COLLECTANEA MATHEMATICA | 2020年 / 71卷 / 02期

关键词：

TENSOR-PRODUCTS; SPACES;

D O I：

10.1007/s13348-019-00261-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 l1spaces 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.

引用

页码：301 / 318

页数：18

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