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

Abstract: In this paper we study properties of functions of triples of not necessarily commuting self-adjoint operators. The main result of the paper shows that unlike in the case of functions of pairs of self-adjoint operators there is no Lipschitz type estimates in the trace norm for arbitrary functions in the Besov class $B_{\infty,1}^1({\Bbb R}^3)$.