Geodesic
Operator Lipschitz functions in several variables and Möbius transformations
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 42, Tome 424 (2014), pp. 5-32 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that if $f$ is an operator Lipschitz function defined on $\mathbb R^n$, then the function $\dfrac{f\circ\varphi}{\|\varphi'\|}$ is also operator Lipschitz for every Möbius transformations $\varphi$ with $f(\varphi(\infty))=0$. Here $\|\varphi'\|$ denotes the operator norm of the Jacobian matrix $\varphi'$. Similar statements are obtained also for operator Lipschitz functions defined on closed subsets of $\mathbb R^n$. 
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     author = {A. B. Aleksandrov},
     title = {Operator {Lipschitz} functions in several variables and {M\"obius} transformations},
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A. B. Aleksandrov. Operator Lipschitz functions in several variables and Möbius transformations. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 42, Tome 424 (2014), pp. 5-32. http://geodesic.mathdoc.fr/item/ZNSL_2014_424_a0/

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