Functions of perturbed tuples of self-adjoint operators

摘要

We generalize earlier results of Aleksandrov and Peller (2010) [2,3], Aleksandrov et al. (2011) [6], Peller (1985) [13], Peller (1990) [14] to the case of functions of n-tuples of commuting self-adjoint operators. In particular, we prove that if a function f belongs to the Besov space B∞,11(Rn), then f is operator Lipschitz and we show that if f satisfies a H?lder condition of order α, then ||f(A _1, ..., A _n)-f(B _1, ..., B _n)||≤constmax 1≤j≤n||A _j-B _j|| α for all n-tuples of commuting self-adjoint operators (A _1, ..., A _n) and (B _1, ..., B _n). We also consider the case of arbitrary moduli of continuity and the case when the operators A _j-B _j belong to the Schatten-von Neumann class S _p.