Trace Formulas for Multivariate Operator Functions

We extend results on Taylor-like approximations of single-variable operator functions of contractions to the multivariate case, with perturbations allowed to be in normed ideals of B(H)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{B}(\mathcal{H})}$$\end{document}. Our results follow from properties of partial derivatives of multivariate operator functions established in the paper.