The Solution of the Kadison-Singer Problem

Опубликовано 18 августа 2016, 19:03

The Kadison-Singer problem is a question in operator theory which arose in 1959 while trying to make Dirac's axioms for quantum mechanics mathematically rigorous in the context of von Neumann algebras. A positive solution to the problem is given by Nikhil Srivastava by proving essentially the strongest possible partitioning theorem of this type. The proof is based on two significant ingredients: a new existence argument, which reduces the problem to bounding the roots of the expected characteristic polynomials of certain random matrices, and a general method for proving upper bounds on the roots of such polynomials. The techniques are elementary, mostly based on tools from the theory of real stable polynomials