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In this paper we study properties of functions of triples of not necessarilycommuting self-adjoint operators. The main result of the paper shows thatunlike in the case of functions of pairs of self-adjoint operators there is noLipschitz type estimates in the trace norm for arbitrary functions in the Besovclass $B_{\infty,1}^1({\Bbb R}^3)$.

Functions of triples of noncommuting self-adjoint operators and their perturbations