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Operator and commutator moduli of continuity for normal operators. / Peller, V. V.; Александров, Алексей Борисович.
в: Proceedings of the London Mathematical Society, Том 105, № 4, 10.2012, стр. 821-851.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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