Title

A New Functional Calculus for Noncommuting Operators

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

Peer Reviewed

1

Copyright

Elsevier