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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
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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

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