From a dichotomy for images to Haagerup's inequality

Details From a dichotomy for images to Haagerup's inequality From a dichotomy for images to Haagerup's inequality

2009-07-17

arxiv.org/abs/0907.2960v2

Mathematics

General Topology

8 pages, 2 figures. Added a general, topological version of the Jordan Filling Principle. Corrected a few minor inaccuracies

Scientific paper

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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