Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-19T11:49:51.898Z Has data issue: false hasContentIssue false
  • English
  • Français

Lower bounds for multilinear forms defined on Hilbert Spaces

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  26 February 2010

Juan Carlos García-Vázquez  and
Rafael Villa
Juan Carlos García-Vázquez
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, Sevilla 41080, Spain. E-mail: garcia@cica.es
Rafael Villa
Affiliation:
Departamento de Análisis Matemático, Facultad de Matematicas, Universidad de Sevilla, Apdo. 1160, Sevilla 41080, Spain. E-mail: rvcaro@cica.es
Get access

Abstract

In this paper, it is proved that, for any m unit vectors. x1…, xm in any n-dimensional real Hilbert space, there exists a unit vector x0 such that

for any y∈Sn−1. The exact value of the above integral is calculated, and these results used to improve some lower bounds for multilinear forms on real Hilbert spaces. An integral expression is also given for the complex case.

MSC classification

Secondary: 46C05: Hilbert and pre-Hilbert spaces
Type
Research Article
Information
Mathematika , Volume 46 , Issue 2 , December 1999 , pp. 315 - 322
Copyright
Copyright © University College London 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[A] de Reyna, J. Arias. Gaussian variables, polynomials and permanents. Lin. Alg. Appl. 285 (1998), 107–114.CrossRefGoogle Scholar
[BS] Benitez, C. and Sarantopoulos, Y.. A polynomial inequality on a Hilbert space. Amer. Math. Monthly (to appear).Google Scholar
[BST] Benitez, C., Sarantopoulos, Y. and Tonge, A.. Lower bounds for norms of products of polynomials. Math. Proc. Cambr. Phil. Soc. 124 (3) (1998).CrossRefGoogle Scholar
[G] Gross, O.. The rendezvous value of a metric space. Ann. Math. Stud. 52 (1964). 49–53.Google Scholar
[LMS] Litvak, A. E., Milman, V. D. and Schechtman, G.. Averages of norms and quasi-norms. Math. Ann., 312 (1998), 95–124.CrossRefGoogle Scholar
[MN] Morris, S. A. and Nickolas, P.. On the average distance property of compact connected metric spaces. Arch. Math., 50 (1983), 459–463.CrossRefGoogle Scholar
[S] Stadje, W.. A property of compact connected spaces. Arch. Math., 36 (1981). 275–280.CrossRefGoogle Scholar