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arXiv · 0708.3594

A new functional calculus for non-commuting operators

F. Colombo·I. Sabadini·D. C. Struppa
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Abstract

In this paper we use the notion of slice monogenic functions \cite{slicecss} to define a new functional calculus for an $n$-tuple $T$ of not necessarily commuting operators. This calculus is different from the one discussed in \cite{jefferies} and it allows the explicit construction of the eigenvalue equation for the $n$-tuple $T$ based on a new notion of spectrum for $T$. Our functional calculus is consistent with the Riesz-Dunford calculus in the case of a single operator.

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F. Colombo, I. Sabadini, D. C. Struppa. 2008-01-25. A new functional calculus for non-commuting operators. https://doi.org/10.1016/j.jfa.2007.12.008

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