Year: 2019
Type: preprint
Abstract: We show that Lieb's concavity theorem holds more generally for any unitarily invariant matrix function $ϕ:\mathbf{H}^n_+\rightarrow \mathbb{R}$ that is monotone and concave. Concretely, we prove the joint concavity of the function $(A,B) \mapstoϕ\big[(B^\frac{qs}{2}K^*A^{ps}KB^\frac{qs}{2})^{\frac{1}{s}}\big] $ on $\mathbf{H}_+^m\times\mathbf{H}_+^n$, for any $K\in \mathbb{C}^{m\times n},s\in(0,1],p,q\in[0,1], p+q\leq 1$.
Source: arXiv (Cornell University)
Author: Huang, De
Institution: California Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2946839014