On Akemann-Weaver Conjecture
Functional Analysis
2023-03-24 v1 Combinatorics
Abstract
Akemann and Weaver showed Lyapunov-type theorem for rank one positive semidefinite matrices which is an extension of Weaver's KS conjecture that was proven by Marcus, Spielman, and Srivastava in their breakthrough solution of the Kadison-Singer problem. They conjectured that a similar result holds for higher rank matrices. We prove the conjecture of Akemann and Weaver by establishing Lyapunov-type theorem for trace class operators. In the process we prove a matrix discrepancy result for sums of hermitian matrices. This extends rank one result of Kyng, Luh, and Song who established an improved bound in Lyapunov-type theorem of Akemann and Weaver.
Keywords
Cite
@article{arxiv.2303.12954,
title = {On Akemann-Weaver Conjecture},
author = {Marcin Bownik},
journal= {arXiv preprint arXiv:2303.12954},
year = {2023}
}