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
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TY - JOUR
T1 - Functions of perturbed pairs of noncommuting contractions
AU - Peller, V. V.
AU - Александров, Алексей Борисович
N1 - Publisher Copyright: © 2020 Russian Academy of Sciences (DoM) and London Mathematical Society.
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