Multicentric holomorphic calculus for $n-$tuples of commuting operators

Document Type: Original Article

Author

Department of Mathematics and Systems Analysis, Aalto University, Otaniemi, Finland

Abstract

‎In multicentric holomorphic calculus, one represents the function $\varphi$ using a new polynomial variable $w=p(z),$ $z\in \mathbb{C},$ in such a way that when it is evaluated at the operator $T,$ then $p(T)$ is small in norm‎. ‎Usually it is assumed that $p$ has distinct roots‎. ‎In this paper we aim to extend this multicentric holomorphic calculus to $n-$tuples of commuting operators looking in particular at the case when $n=2$‎.

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