Strong Haagerup inequalities for free R-diagonal elements

Details Strong Haagerup inequalities for free R-diagonal elements Strong Haagerup inequalities for free R-diagonal elements

2005-12-21

arxiv.org/abs/math/0512481v2

Mathematics

Operator Algebras

27 pages, 8 figures

Scientific paper

In this paper, we generalize Haagerup's inequality (on convolution norm in the free group) to a very general context of R-diagonal elements in a tracial von Neumann algebra; moreover, we show that in this "holomorphic" setting, the inequality is greatly improved from its originial form. We give an elementary combinatorial proof of a very special case of our main result, and then generalize these techniques. En route, we prove a number of moment and cumulant estimates for R-diagonal elements that are of independent interest. Finally, we use our strong Haagerup inequality to prove a strong ultracontractivity theorem.

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