Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590167 | Journal of Functional Analysis | 2014 | 31 Pages |
Abstract
Let (A1,â¦,An) and (B1,â¦,Bn) be n-tuples of commuting self-adjoint operators on Hilbert space. For functions f on Rn satisfying certain conditions, we obtain sharp estimates of the operator norms (or norms in operator ideals) of f(A1,â¦,An)âf(B1,â¦,Bn) in terms of the corresponding norms of AjâBj, 1⩽j⩽n. We obtain analogs of earlier results on estimates for functions of perturbed self-adjoint and normal operators. It turns out that for n⩾3, the methods that were used for self-adjoint and normal operators do not work. We propose a new method that works for arbitrary n. We also get sharp estimates for quasicommutators f(A1,â¦,An)RâRf(B1,â¦,Bn) in terms of norms of AjRâRBj, 1⩽j⩽n, for a bounded linear operator R.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
F.L. Nazarov, V.V. Peller,