On Akemann-Weaver Conjecture
arXiv (Cornell University)(2023)
Abstract
Akemann and Weaver showed Lyapunov-type theorem for rank one positive semidefinite matrices which is an extension of Weaver's KS$_2$ 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.
MoreTranslated text
Key words
akemann-weaver
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined