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.
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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.