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arXiv · 1808.08566

Functions of perturbed pairs of noncommuting contractions

Aleksei Aleksandrov·Vladimir Peller
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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 $(B_{\infty,1}^1)_+({\Bbb D}^2)$ 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 $\boldsymbol{S}_p$ for $p\in[1,2]$. On the other hand, we show that for functions in the Besov space $(B_{\infty,1}^1)_+({\Bbb D}^2)$, there are no Lipschitz such type estimates for $p>2$ as well as in the operator norm.

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BibTeXRIS

Aleksei Aleksandrov, Vladimir Peller. 2018-08-26. Functions of perturbed pairs of noncommuting contractions. https://arxiv.org/abs/1808.08566

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