Functions of Perturbed Noncommuting Self-adjoint Operators
نویسندگان
چکیده
Abstract. We consider functions f(A,B) of noncommuting self-adjoint operators A and B that can be defined in terms of double operator integrals. We prove that if f belongs to the Besov class B ∞,1 (R), then we have the following Lipschitz type estimate in the trace norm: ‖f(A1, B1)− f(A2, B2)‖S1 ≤ const(‖A1 −A2‖S1 + ‖B1 −B2‖S1). However, the condition f ∈ B ∞,1 (R) does not imply the Lipschitz type estimate in the operator norm.
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