Optimal estimates for summing multilinear operators

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.

Keywords:

• Multiple summing operators
• Banach spaces

AMS Subject Classifications:

• 47B10
• 47L22
• 46G25

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.