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arXiv · 1801.02934

Unitarily invariant norm inequalities involving $G_1$ operators

Mojtaba Bakherad
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Abstract

In this paper, we present some upper bounds for unitarily invariant norms inequalities. Among other inequalities, we show some upper bounds for the Hilbert-Schmidt norm. In particular, we prove \begin{align*} \|f(A)Xg(B)\pm g(B)Xf(A)\|_2\leq \left\|\frac{(I+|A|)X(I+|B|)+(I+|B|)X(I+|A|)}{d_Ad_B}\right\|_2, \end{align*} where $A, B, X\in\mathbb{M}_n$ such that $A$, $B$ are Hermitian with $σ(A)\cupσ(B)\subset\mathbb{D}$ and $f, g$ are analytic on the complex unit disk $\mathbb{D}$, $g(0)=f(0)=1$, $\textrm{Re}(f)>0$ and $\textrm{Re}(g)>0$.

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Mojtaba Bakherad. 2018-01-09. Unitarily invariant norm inequalities involving $G_1$ operators. https://arxiv.org/abs/1801.02934

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