In this paper we use the notion of slice monogenic functions [F. Colombo, I. Sabadini, D.C. Struppa, Slice monogenic functions, Israel J. Math., in press] 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 [B. Jefferies, Spectral Properties of Noncommuting Operators, Lecture Notes in Math., vol. 1843, Springer-Verlag, Berlin, 2004] 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. © 2008 Elsevier Inc. All rights reserved.
Colombo, F., Sabadini, I., & Struppa, D. C. (2008). A new functional calculus for noncommuting operators. Journal of Functional Analysis, 254(8), 2255–2274. https://doi.org/10.1016/j.jfa.2007.12.008