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 for . On the other hand, we show that for functions in , there are no such Lipschitz type estimates for , nor in the operator norm.
ISSN: 1468-4810
Izvestiya: Mathematics is the English edition of the Russian bimonthly journal Izvestiya Rossiiskoi Akademii Nauk, Seriya Matematicheskaya, founded in 1937. Izvestiya: Mathematics has been published in partnership with Turpion Ltd since 1995. The journal publishes only original research papers containing full results in the author's field of study.
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