Hyperbolic polynomials and the Kadison-Singer problem
Abstract
Recently Marcus, Spielman and Srivastava gave a spectacular proof of a theorem which implies a positive solution to the Kadison-Singer problem via Weaver's KSr conjecture. We extend this theorem to the realm of hyperbolic polynomials and hyperbolicity cones, as well as to arbitrary ranks. We also sharpen the theorem by providing better bounds, which imply better bounds in Weaver's KSr conjecture for each r>2. For r=2 our bound agrees with Bownik et al.
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