Functions of noncommuting operators under perturbation of class Sp

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Functions of noncommuting operators under perturbation of class S_p. / Aleksandrov, A. B.; Peller, V. V.

In: Mathematische Nachrichten, Vol. 293, No. 5, 01.05.2020, p. 847-860.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{ee5e530b11874999a9be9ce6aa18eba8,

title = "Functions of noncommuting operators under perturbation of class Sp",

abstract = "In this article we prove that for (Formula presented.), there exist pairs of self-adjoint operators (Formula presented.) and (Formula presented.) and a function f on the real line in the homogeneous Besov class (Formula presented.) such that the differences (Formula presented.) and (Formula presented.) belong to the Schatten–von Neumann class Sp but (Formula presented.). 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 (Formula presented.).",

keywords = "46E35, 47A20, 47A55, 47A60, 47A63, Besov classes, contractions, double operator integrals, functions of noncommuting operators, Schatten–von Neumann classes, self-adjoint operators, triple operator integrals",

author = "Aleksandrov, {A. B.} and Peller, {V. V.}",

note = "Publisher Copyright: {\textcopyright} 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim",

year = "2020",

month = may,

day = "1",

doi = "10.1002/mana.201900074",

language = "English",

volume = "293",

pages = "847--860",

journal = "Mathematische Nachrichten",

issn = "0025-584X",

publisher = "Wiley-Blackwell",

number = "5",

}

RIS

TY - JOUR

T1 - Functions of noncommuting operators under perturbation of class Sp

AU - Aleksandrov, A. B.

AU - Peller, V. V.

PY - 2020/5/1

Y1 - 2020/5/1

N2 - In this article we prove that for (Formula presented.), there exist pairs of self-adjoint operators (Formula presented.) and (Formula presented.) and a function f on the real line in the homogeneous Besov class (Formula presented.) such that the differences (Formula presented.) and (Formula presented.) belong to the Schatten–von Neumann class Sp but (Formula presented.). 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 (Formula presented.).

AB - In this article we prove that for (Formula presented.), there exist pairs of self-adjoint operators (Formula presented.) and (Formula presented.) and a function f on the real line in the homogeneous Besov class (Formula presented.) such that the differences (Formula presented.) and (Formula presented.) belong to the Schatten–von Neumann class Sp but (Formula presented.). 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 (Formula presented.).

KW - 46E35

KW - 47A20

KW - 47A55

KW - 47A60

KW - 47A63

KW - Besov classes

KW - contractions

KW - double operator integrals

KW - functions of noncommuting operators

KW - Schatten–von Neumann classes

KW - self-adjoint operators

KW - triple operator integrals

UR - http://www.scopus.com/inward/record.url?scp=85080067826&partnerID=8YFLogxK

U2 - 10.1002/mana.201900074

DO - 10.1002/mana.201900074

M3 - Article

VL - 293

SP - 847

EP - 860

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

IS - 5

ER -

ID: 78407240