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∞,11(R2), 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∞,11(R2) does not imply the Lipschitz-type estimate in the operator norm.
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