Israel Journal of Mathematics

, Volume 60, Issue 2, pp 199–224

A new upper bound for the complex Grothendieck constant

  • Uffe Haagerup
Article

DOI: 10.1007/BF02790792

Cite this article as:
Haagerup, U. Israel J. Math. (1987) 60: 199. doi:10.1007/BF02790792

Abstract

Let ϕ denote the real function
$$\varphi (k) = k\smallint _0^{\pi /2} \frac{{cos^2 t}}{{\sqrt {1 - k^2 sin ^2 t} }}dt, - 1 \leqq k \leqq 1$$
and letKGC be the complex Grothendieck constant. It is proved thatKGC≦8/π(k0+1), wherek0 is the (unique) solution to the equationϕ(k)=1/8π(k+1) in the interval [0,1]. One has 8/π(k0+1) ≈ 1.40491. The previously known upper bound isKGCe1−y ≈ 1.52621 obtained by Pisier in 1976.

Copyright information

© The Weizmann Science Press of Israel 1987

Authors and Affiliations

  • Uffe Haagerup
    • 1
  1. 1.Mathematisk InstitutOdense UniversityOdense MDenmark