On Akemann-Weaver Conjecture

2023/03/22 by Marcin Bownik, Bownik, Marcin · 1 citation
Mathematics · #Mathematical Approximation and Integration #Approximation Theory and Sequence Spaces #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2303.12954

Abstract

Akemann and Weaver showed Lyapunov-type theorem for rank one positive semidefinite matrices which is an extension of Weaver's KS₂ 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.

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