Bounded perturbations of Bernstein functions of several operator variables
A. R. Mirotin
TL;DR
This paper investigates bounded perturbations of Bernstein functions applied to multiple operator variables, establishing conditions for differentiability, commutator estimates, and extending trace formulas within the functional calculus framework.
Contribution
It introduces new conditions for Lipschitzness and Frechet-differentiability of Bernstein functions of several operators, generalizes trace formulas, and provides operator norm estimates.
Findings
Conditions for Lipschitzness and Frechet-differentiability established
Norm estimates for commutators derived
Generalization of Livschits-Kre28n trace formula achieved
Abstract
The paper deals with (multidimensional and one-dimensional) Bochner-Phillips functional calculus. Bounded perturbations of Bernstein functions of (one or several commuting) semigroup generators on Banach spaces are considered, conditions for Lipschitzness and Frechet-differentiability of such functions are obtained, estimates for the norm of commutators are proved, and a generalization of Livschits-Kre\u{\i}n trace formula derived.
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Advanced Banach Space Theory · Advanced Numerical Analysis Techniques