Functions of Perturbed Tuples of Self-adjoint Operators
نویسندگان
چکیده
Abstract. We generalize earlier results of [2], [3], [6], [13], [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 ∞,1(R ), then f is operator Lipschitz and we show that if f satisfies a Hölder condition of order α, then ‖f(A1 · · · , An)− f(B1, · · · , Bn)‖ ≤ constmax1≤j≤n ‖Aj −Bj‖ α for all n-tuples of commuting self-adjoint operators (A1, · · · , An) and (B1, · · · , Bn). We also consider the case of arbitrary moduli of continuity and the case when the operators Aj −Bj belong to the Schatten–von Neumann class Sp.
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