Advances in Operator Theory

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

ِDiana Andrei

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‎‎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 $n=2$‎.

Article information

Adv. Oper. Theory, Volume 4, Number 2 (2019), 447-461.

Received: 16 April 2018
Accepted: 2 October 2018
First available in Project Euclid: 1 December 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 47A60: Functional calculus
Secondary: 46E20‎ ‎47A13‎ ‎47A25

multicentric calculus‎‎ ‎commuting operator ‎ ‎lemniscate‎ ‎ ‎von Neumann's inequality‎ ‎ ‎homogeneous polynomial


Andrei, ِDiana. Multicentric holomorphic calculus for $n-$tuples of commuting operators. Adv. Oper. Theory 4 (2019), no. 2, 447--461. doi:10.15352/aot.1804-1346.

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