A generalisation to Birkhoff - von Neumann theorem

Liviu Paunescu; Florin Radulescu

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arXiv · 1506.01685

A generalisation to Birkhoff - von Neumann theorem

Liviu Paunescu·Florin Radulescu

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Abstract

The classic Birkhoff- von Neumann theorem states that the set of doubly stochastic matrices is the convex hull of the permutation matrices. In this paper, we study a generalisation of this theorem in the type $II_1$ setting. Namely, we replace a doubly stochastic matrix with a collection of measure preserving partial isomorphisms, of the unit interval, with similar properties. We show that a weaker version of this theorem still holds.

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Liviu Paunescu, Florin Radulescu. 2015-06-04. A generalisation to Birkhoff - von Neumann theorem. https://arxiv.org/abs/1506.01685

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