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Articles

Optimal estimates for summing multilinear operators

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Pages 930-942 | Received 12 Sep 2015, Accepted 19 Jul 2016, Published online: 05 Aug 2016
 

Abstract

We show that given a positive integer m, a real number and the set of non-multiple -summing m-linear forms on contains, except for the null vector, a closed subspace of maximal dimension whenever . This result is optimal since for all m-linear forms on are multiple -summing. In particular, among other results, we generalize a result related to cotype (from 2010) due to Botelho, Michels and the second named author.

AMS Subject Classifications:

Acknowledgements

The authors are very grateful to the two referees for their important comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.

Present address: Departamento de Matemática, Universidade Estadual da Parariba, Campina Grande, Brazil.

Additional information

Funding

D. Pellegrino was supported by CNPq.

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