Journal of Mathematical Sciences

, Volume 209, Issue 5, pp 665–682 | Cite as

Operator Lipschitz Functions in Several Variables and Möbius Transformations

  • A. B. Aleksandrov

It is proved that if f is an operator Lipschitz function defined on n , then the function \( \frac{f\circ \varphi }{\left\Vert {\varphi}^{\prime}\right\Vert } \) is also operator Lipschitz for every Möbius transformation φ with f(φ(∞)) = 0. Hereφ′‖ denotes the operator norm of the Jacobian matrix φSimilar statements for operator Lipschitz functions defined on closed subsets of n are also obtained. Bibliography: 10 titles.


Closed Subset Homogeneous Polynomial Orthogonal Transformation Linear Fractional Transformation Joint Spectrum 
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.St.Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia

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