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Diniz, D. and Muñoz-Fernández, Gustavo A. and Pellegrino, D. and Seoane-Sepúlveda, Juan B.
(2014)
*Lower bounds for the constants in the Bohnenblust-Hille inequality: the case of real scalars.*
Proceedings of the American Mathematical Society, 142
(2).
pp. 575-580.
ISSN 0002-9939

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Official URL: http://www.ams.org/journals/proc/2014-142-02/S0002-9939-2013-11791-0/S0002-9939-2013-11791-0.pdf

## Abstract

The Bohnenblust-Hille inequality was obtained in 1931 and ( in the case of real scalars) asserts that for every positive integer m there is a constant Cm so that

((N)Sigma(i1 , . . . , im=1)vertical bar T(e(i1) (,...,) e(im))vertical bar(2m/m+1))(m+1/2) <= C-m parallel to T parallel to

for all positive integers N and every m-linear mapping T : l(infinity)(N) x...x l(infinity)(N) -> R. Since then, several authors have obtained upper estimates for the values of C-m. However, the novelty presented in this short note is that we provide lower (and non-trivial) bounds for C-m.

Item Type: | Article |
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Uncontrolled Keywords: | Absolutely summing operators; Bohnenblust-Hille Theorem; Bohnenblust-Hille inequality |

Subjects: | Sciences > Mathematics > Algebra |

ID Code: | 24705 |

Deposited On: | 17 Mar 2014 12:33 |

Last Modified: | 28 Nov 2016 08:13 |

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