Standard

Operator and commutator moduli of continuity for normal operators. / Peller, V. V.; Александров, Алексей Борисович.

In: Proceedings of the London Mathematical Society, Vol. 105, No. 4, 10.2012, p. 821-851.

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

Harvard

Peller, VV & Александров, АБ 2012, 'Operator and commutator moduli of continuity for normal operators', Proceedings of the London Mathematical Society, vol. 105, no. 4, pp. 821-851. https://doi.org/10.1112/plms/pds012

APA

Peller, V. V., & Александров, А. Б. (2012). Operator and commutator moduli of continuity for normal operators. Proceedings of the London Mathematical Society, 105(4), 821-851. https://doi.org/10.1112/plms/pds012

Vancouver

Peller VV, Александров АБ. Operator and commutator moduli of continuity for normal operators. Proceedings of the London Mathematical Society. 2012 Oct;105(4):821-851. https://doi.org/10.1112/plms/pds012

Author

Peller, V. V. ; Александров, Алексей Борисович. / Operator and commutator moduli of continuity for normal operators. In: Proceedings of the London Mathematical Society. 2012 ; Vol. 105, No. 4. pp. 821-851.

BibTeX

@article{339dfe0e8cdd4c458a9c9bd6423657be,
title = "Operator and commutator moduli of continuity for normal operators",
abstract = "We study in this paper properties of functions of perturbed normal operators and develop earlier results obtained in Aleksandrov, Peller, Potapov and Sukochev ['Functions of normal operators under perturbations', Adv. Math. 226 (2011) 5216-5251.]. We study operator Lipschitz and commutator Lipschitz functions on closed subsets of the plane. For such functions we introduce the notions of the operator modulus of continuity and of various commutator moduli of continuity. Our estimates lead to estimates of the norms of quasicommutators f(N 1)R-Rf(N 2) in terms of N 1R-RN 2, where N 1 and N 2 are normal operator and R is a bounded linear operator. In particular, we show that if 0 < α < 1 and f is a H{\"o}lder function of order α, then, for normal operators N 1 and N 2, In the last section, we obtain lower estimates for constants in operator H{\"o}lder estimates.",
author = "Peller, {V. V.} and Александров, {Алексей Борисович}",
note = "Funding Information: The first author is partially supported by RFBR grant 11-01-00526-a; the second author is partially supported by NSF grant DMS 1001844.",
year = "2012",
month = oct,
doi = "10.1112/plms/pds012",
language = "English",
volume = "105",
pages = "821--851",
journal = "Proceedings of the London Mathematical Society",
issn = "0024-6115",
publisher = "Oxford University Press",
number = "4",

}

RIS

TY - JOUR

T1 - Operator and commutator moduli of continuity for normal operators

AU - Peller, V. V.

AU - Александров, Алексей Борисович

N1 - Funding Information: The first author is partially supported by RFBR grant 11-01-00526-a; the second author is partially supported by NSF grant DMS 1001844.

PY - 2012/10

Y1 - 2012/10

N2 - We study in this paper properties of functions of perturbed normal operators and develop earlier results obtained in Aleksandrov, Peller, Potapov and Sukochev ['Functions of normal operators under perturbations', Adv. Math. 226 (2011) 5216-5251.]. We study operator Lipschitz and commutator Lipschitz functions on closed subsets of the plane. For such functions we introduce the notions of the operator modulus of continuity and of various commutator moduli of continuity. Our estimates lead to estimates of the norms of quasicommutators f(N 1)R-Rf(N 2) in terms of N 1R-RN 2, where N 1 and N 2 are normal operator and R is a bounded linear operator. In particular, we show that if 0 < α < 1 and f is a Hölder function of order α, then, for normal operators N 1 and N 2, In the last section, we obtain lower estimates for constants in operator Hölder estimates.

AB - We study in this paper properties of functions of perturbed normal operators and develop earlier results obtained in Aleksandrov, Peller, Potapov and Sukochev ['Functions of normal operators under perturbations', Adv. Math. 226 (2011) 5216-5251.]. We study operator Lipschitz and commutator Lipschitz functions on closed subsets of the plane. For such functions we introduce the notions of the operator modulus of continuity and of various commutator moduli of continuity. Our estimates lead to estimates of the norms of quasicommutators f(N 1)R-Rf(N 2) in terms of N 1R-RN 2, where N 1 and N 2 are normal operator and R is a bounded linear operator. In particular, we show that if 0 < α < 1 and f is a Hölder function of order α, then, for normal operators N 1 and N 2, In the last section, we obtain lower estimates for constants in operator Hölder estimates.

UR - http://www.scopus.com/inward/record.url?scp=84868020172&partnerID=8YFLogxK

U2 - 10.1112/plms/pds012

DO - 10.1112/plms/pds012

M3 - Article

VL - 105

SP - 821

EP - 851

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 4

ER -

ID: 5415461