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Interpolation by the Derivatives of Operator Lipschitz Functions

  • A. B. Aleksandrov
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 261)

Abstract

Let Λ be a discrete subset of the real line ℝ. We prove that for every bounded function φ on Λ there exists an operator Lipschitz function f on ℝ such that f’ (t) = φ(t) for all t∈Λ. The same is true for the set of operator Lipschitz functions f on ℝ such that f’ coincides with the non-tangential boundary values of a bounded holomorphic function on the upper half-plane. In other words, for every bounded function φ on Λ there exists a commutator Lipschitz function f on the closed upper half-plane such that f’ (t) = φ(t) for all t∈Λ. The same is also true for some non-discrete countable sets Λ. Furthermore, we consider the case where Λ is a subset of the closed upper half-plane, Λ ℝ. Similar questions for commutator Lipschitz functions on a closed subset F of ℂ are also considered.

Keywords

Operator Lipschitz functions commutator Lipschitz functions interpolation 

Mathematics Subject Classification (2010)

Primary 47A56 Secondary 30H05 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Saint PetersburgRussia

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