• Corpus ID: 146808043

Improvement on a Generalized Lieb's Concavity Theorem

@article{Huang2019ImprovementOA,
  title={Improvement on a Generalized Lieb's Concavity Theorem},
  author={De Huang},
  journal={arXiv: Functional Analysis},
  year={2019}
}
  • De Huang
  • Published 4 May 2019
  • Mathematics
  • arXiv: Functional Analysis
We show that Lieb's concavity theorem holds more generally for any unitary invariant matrix function $\phi:\mathbf{H}_+^n\rightarrow \mathbb{R}_+^n$ that is concave and satisfies Holder's inequality. Concretely, we prove the joint concavity of the function $(A,B) \mapsto\phi\big[(B^\frac{qs}{2}K^*A^{ps}KB^\frac{qs}{2})^{\frac{1}{s}}\big] $ on $\mathbf{H}_+^n\times\mathbf{H}_+^m$, for any $K\in \mathbb{C}^{n\times m}$ and any $s,p,q\in(0,1], p+q\leq 1$. This result improves a recent work by… 

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  • De Huang
  • Mathematics
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  • 2019

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