On a Trace Formula for Functions of Noncommuting Operators

Standard

On a Trace Formula for Functions of Noncommuting Operators. / Александров, Алексей Борисович ; Peller, V. V.; Potapov, D. S.

In: Mathematical Notes, Vol. 106, No. 3-4, 01.09.2019, p. 481-487.

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

BibTeX

@article{9aa6fcf15223426caea2542183b48c49,

title = "On a Trace Formula for Functions of Noncommuting Operators",

abstract = "The main result of the paper is that the Lifshits-Krein trace formula cannot be generalized to the case of functions of noncommuting self-adjoint operators. To prove this, we show that, for pairs (A1, B1) and (A2, B2) of bounded self-adjoint operators with trace class differences A2-A1 and B2-B1, it is impossible to estimate the modulus of the trace of the difference f (A2, B2) - f (A1, B1) in terms of the norm of f in the Lipschitz class.",

keywords = "Lifshits-Krein trace formula, operators Lipschitz functions, trace, trace class operators",

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

note = "Publisher Copyright: {\textcopyright} 2019, Pleiades Publishing, Ltd.",

year = "2019",

month = sep,

day = "1",

doi = "10.1134/S0001434619090189",

language = "English",

volume = "106",

pages = "481--487",

journal = "Mathematical Notes",

issn = "0001-4346",

publisher = "Pleiades Publishing",

number = "3-4",

}

RIS

TY - JOUR

T1 - On a Trace Formula for Functions of Noncommuting Operators

AU - Александров, Алексей Борисович

AU - Peller, V. V.

AU - Potapov, D. S.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - The main result of the paper is that the Lifshits-Krein trace formula cannot be generalized to the case of functions of noncommuting self-adjoint operators. To prove this, we show that, for pairs (A1, B1) and (A2, B2) of bounded self-adjoint operators with trace class differences A2-A1 and B2-B1, it is impossible to estimate the modulus of the trace of the difference f (A2, B2) - f (A1, B1) in terms of the norm of f in the Lipschitz class.

AB - The main result of the paper is that the Lifshits-Krein trace formula cannot be generalized to the case of functions of noncommuting self-adjoint operators. To prove this, we show that, for pairs (A1, B1) and (A2, B2) of bounded self-adjoint operators with trace class differences A2-A1 and B2-B1, it is impossible to estimate the modulus of the trace of the difference f (A2, B2) - f (A1, B1) in terms of the norm of f in the Lipschitz class.

KW - Lifshits-Krein trace formula

KW - operators Lipschitz functions

KW - trace

KW - trace class operators

UR - http://www.scopus.com/inward/record.url?scp=85074101503&partnerID=8YFLogxK

U2 - 10.1134/S0001434619090189

DO - 10.1134/S0001434619090189

M3 - Article

AN - SCOPUS:85074101503

VL - 106

SP - 481

EP - 487

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 3-4

ER -

ID: 87314853