A new functional calculus for non-commuting operators
arXiv:0708.3594 · doi:10.1016/j.jfa.2007.12.008
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.
to appear in Journal of Functional Analysis