The linear polarization constant of R n

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Abstract

He present work deals with estimations of the n-th linear polarization constant c(H) n of an n-dimensional real Hilbert space H. We provide some new lower bounds on the value of sup ∥y∥=1 |〈x 1,y〉 ... 〈x n,y〉|, where x 1, ... ,x n are unit vectors in H. In particular, the results improve an earlier estimate of Marcus. However, the intriguing conjecture c(H) n= n n/2 remains open.

Original languageEnglish
Pages (from-to)129-136
Number of pages8
JournalActa Mathematica Hungarica
Volume108
Issue number1-2
DOIs
Publication statusPublished - Jul 1 2005

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Keywords

  • Gram matrices
  • Linear polarization constants
  • Polynomials over normed spaces

ASJC Scopus subject areas

  • Mathematics(all)

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