A New Functional Calculus for Noncommuting Operators

Authors

Fabrizio Colombo, Politecnico di Milano
Irene Sabadini, Politecnico di Milano
Daniele C. Struppa, Chapman UniversityFollow

Document Type

Article

Publication Date

2008

Abstract

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.

Comments

This article was originally published in Journal of Functional Analysis, volume 254, issue 8, in 2008. DOI: 10.1016/j.jfa.2007.12.008

Recommended Citation

Colombo, F., Sabadini, I., & Struppa, D. C. (2008). A new functional calculus for noncommuting operators. Journal of Functional Analysis, 254(8), 2255-2274. doi: 10.1016/j.jfa.2007.12.008

Peer Reviewed

1

Copyright

Elsevier