Functions of perturbed pairs of noncommuting contractions

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Functions of perturbed pairs of noncommuting contractions. / Peller, V. V.; Александров, Алексей Борисович.

In: Izvestiya Mathematics, Vol. 84, No. 4, 08.2020, p. 659-682.

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

BibTeX

@article{70cdcfaba0cf422dbe03578712e8d34e,

title = "Functions of perturbed pairs of noncommuting contractions",

abstract = "We consider functions of pairs of noncommuting contractions on Hilbert space and study the problem as to which functions we have Lipschitz type estimates in Schatten-von Neumann norms. We prove that if belongs to the Besov class of analytic functions in the bidisc, then we have a Lipschitz type estimate for functions of pairs of not necessarily commuting contractions in the Schatten-von Neumann norms. On the other hand, we show that for functions in, there are no such Lipschitz type estimates for, nor in the operator norm.",

keywords = "Besov classes, contractions, double operator integrals, Haagerup tensor products, Haagerup-like tensor products, perturbation, Schatten von Neumann classes, semi-spectral measures, triple operator integrals",

author = "Peller, {V. V.} and Александров, {Алексей Борисович}",

note = "Publisher Copyright: {\textcopyright} 2020 Russian Academy of Sciences (DoM) and London Mathematical Society.",

year = "2020",

month = aug,

doi = "10.1070/IM8876",

language = "English",

volume = "84",

pages = "659--682",

journal = "Izvestiya Mathematics",

issn = "1064-5632",

publisher = "IOP Publishing Ltd.",

number = "4",

}

RIS

TY - JOUR

T1 - Functions of perturbed pairs of noncommuting contractions

AU - Peller, V. V.

AU - Александров, Алексей Борисович

PY - 2020/8

Y1 - 2020/8

N2 - We consider functions of pairs of noncommuting contractions on Hilbert space and study the problem as to which functions we have Lipschitz type estimates in Schatten-von Neumann norms. We prove that if belongs to the Besov class of analytic functions in the bidisc, then we have a Lipschitz type estimate for functions of pairs of not necessarily commuting contractions in the Schatten-von Neumann norms. On the other hand, we show that for functions in, there are no such Lipschitz type estimates for, nor in the operator norm.

AB - We consider functions of pairs of noncommuting contractions on Hilbert space and study the problem as to which functions we have Lipschitz type estimates in Schatten-von Neumann norms. We prove that if belongs to the Besov class of analytic functions in the bidisc, then we have a Lipschitz type estimate for functions of pairs of not necessarily commuting contractions in the Schatten-von Neumann norms. On the other hand, we show that for functions in, there are no such Lipschitz type estimates for, nor in the operator norm.

KW - Besov classes

KW - contractions

KW - double operator integrals

KW - Haagerup tensor products

KW - Haagerup-like tensor products

KW - perturbation

KW - Schatten von Neumann classes

KW - semi-spectral measures

KW - triple operator integrals

UR - http://www.scopus.com/inward/record.url?scp=85093919164&partnerID=8YFLogxK

U2 - 10.1070/IM8876

DO - 10.1070/IM8876

M3 - Article

AN - SCOPUS:85093919164

VL - 84

SP - 659

EP - 682

JO - Izvestiya Mathematics

JF - Izvestiya Mathematics

SN - 1064-5632

IS - 4

ER -

ID: 87314515