From a dichotomy for images to Haagerup's inequality

Iosif Pinelis

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arXiv · 0907.2960

From a dichotomy for images to Haagerup's inequality

Iosif Pinelis

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Abstract

Let X be a compact topological space, and let D be a subset of X. Let Y be a Hausdorff topological space. Let f be a continuous map of the closure of D to Y such that f(D) is open. Let E be any connected subset of the complement (to Y) of the boundary of D. Then f(D) either contains E or is contained in the complement of E. Applications of this dichotomy principle are given, in particular for holomorphic maps, including maximum and minimum modulus principles, an inverse boundary correspondence, and a proof of Haagerup's inequality for the absolute power moments of linear combinations of independent Rademacher random variables.

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Iosif Pinelis. 2009-07-17. From a dichotomy for images to Haagerup's inequality. https://arxiv.org/abs/0907.2960

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