An Elementary Approach to Operator Lipschitz Type Estimates

Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 261)

Abstract

The paper brings an elementary approach to Lipschitz type estimates for functions of operators. The approach is based on the reduction to the case of operators on finite-dimensional inner product spaces. This allows us to avoid double and triple operator integrals and consider instead double and triple operator sums. Unlike in the case of double and triple operator integrals, double and triple operator sums can be defined for arbitrary functions which completely eliminates the problem of definitions of double operator integrals and various types of triple operator integrals.

Keywords

Functions of commuting operators functions of noncommuting operators Lipschitz type estimates functions of perturbed operators double operator sums triple operator sums Besov spaces 

Mathematics Subject Classification (2010)

Primary 47A55 Secondary 47A60 47A63 47B10 46E39 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsMichigan State UniversityMichiganUSA

Personalised recommendations