Hyperbolic polynomials and the Kadison-Singer problem
Year: 2018
Type: preprint
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 $KS_r$ 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 $KS_r$ conjecture for each $r>2$. For $r=2$ our bound agrees with Bownik et al.
Source: arXiv (Cornell University)
Author: Brändén, Petter
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2889876829