Functions of perturbed tuples of self-adjoint operators (Q424739)

In this paper, the behaviour of functions of perturbed tuples of commuting self-adjoint operators is studied. The results are based on those given especially by Alexandrov and Peller in various cases. The paper presents in the first section the previously obtained results. Using the representation of \(f(A_1,\dots,A_n)-f(B_1,\dots, B_n)\) in terms of double operator integrals, obtained in the second section, in the third section norm estimates are given for \(f(A_1,\dots,A_n)-f(B_1,\dots, B_n)\), where \((A_1,\dots,A_n)\) and \((B_1,\dots, B_n)\) are \(n\)-tuples of commuting operators. Also, in the fourth section norm estimates are obtained in the case of the Schatten-von Neumann class.