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 II1setting. 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 hold
Paunescu, L., Radulescu, F. (2017). A generalisation to Birkhoff–von Neumann theorem. ADVANCES IN MATHEMATICS, 308, 836-858 [10.1016/j.aim.2016.12.031].
A generalisation to Birkhoff–von Neumann theorem
RADULESCU, FLORIN
2017-01-01
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 II1setting. 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 holdFile in questo prodotto:
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