Abstract:
We consider functions f(T,R)f(T,R) of pairs of noncommuting contractions on Hilbert space and study the problem as to which functions ff we have Lipschitz type estimates in Schatten–von Neumann norms. We prove that if ff belongs to the Besov class (B1∞,1)+(T2) of analytic functions in the bidisc, then
we have a Lipschitz type estimate for functions f(T,R) of pairs of not necessarily commuting contractions (T,R) in the Schatten–von Neumann norms Sp for p∈[1,2]. On the other hand, we show that for functions in (B1∞,1)+(T2), there are no such Lipschitz type estimates for p>2, nor in the operator norm.
The research of the first author was partially supported by RFBR grant no. 17-01-00607A.
The publication was prepared with the support of the RUDN University Program “5-100”.