Functions of perturbed pairs of noncommuting contractions

2018/08/26 by Aleksandrov, Aleksei, Peller, Vladimir
#Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1808.08566

Abstract

We consider functions f(T,R) of pairs of noncommuting contractions on Hilbert space and study the problem for which functions f we have Lipschitz type estimates in Schatten--von Neumann norms. We prove that if f belongs to the Besov class (B_∞,1¹)₊(\Bbb D²) of analytic functions in the bidisk, 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 \boldsymbolS_p for p∈[1,2]. On the other hand, we show that for functions in the Besov space (B_∞,1¹)₊(\Bbb D²), there are no Lipschitz such type estimates for p>2 as well as in the operator norm.

Related

• Functions of commuting contractions under perturbation
• Functions of pairs of unbounded noncommuting self-adjoint operators under perturbation
• Functions of perturbed noncommuting unbounded self-adjoint operators
• Functions of noncommuting operators under perturbation of class \boldsymbolS_p
• Functions of perturbed noncommuting self-adjoint operators