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Functions of noncommuting operators under perturbation of class S p
Author(s) -
Aleksandrov A. B.,
Peller V. V.
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900074
Subject(s) - mathematics , class (philosophy) , von neumann architecture , pure mathematics , perturbation (astronomy) , homogeneous , operator theory , algebra over a field , mathematical analysis , combinatorics , physics , quantum mechanics , artificial intelligence , computer science
In this article we prove that for p > 2 , there exist pairs of self‐adjoint operators ( A 1 , B 1 ) and ( A 2 , B 2 ) and a function f on the real line in the homogeneous Besov classB ∞ , 1 1 ( R 2 )such that the differencesA 2 − A 1andB 2 − B 1belong to the Schatten–von Neumann class S p but f ( A 2 , B 2 ) − f ( A 1 , B 1 ) ∉ S p . A similar result holds for functions of contractions. We also obtain an analog of this result in the case of triples of self‐adjoint operators for any p ≥ 1 .