Abstract
Let ϕ denote the real function
and letK CG be the complex Grothendieck constant. It is proved thatK CG ≦8/π(k 0+1), wherek 0 is the (unique) solution to the equationϕ(k)=1/8π(k+1) in the interval [0,1]. One has 8/π(k 0+1) ≈ 1.40491. The previously known upper bound isK CG ≦e 1−y ≈ 1.52621 obtained by Pisier in 1976.
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Haagerup, U. A new upper bound for the complex Grothendieck constant. Israel J. Math. 60, 199–224 (1987). https://doi.org/10.1007/BF02790792
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DOI: https://doi.org/10.1007/BF02790792