Non commutative functional calculus: unbounded operators
Spectral Theory
2015-05-13 v2
Abstract
In a recent work, \cite{cgss}, we developed a functional calculus for bounded operators defined on quaternionic Banach spaces. In this paper we show how the results from \cite{cgss} can be extended to the unbounded case, and we highlight the crucial differences between the two cases. In particular, we deduce a new eigenvalue equation, suitable for the construction of a functional calculus for operators whose spectrum is not necessarily real.
Cite
@article{arxiv.0708.3592,
title = {Non commutative functional calculus: unbounded operators},
author = {F. Colombo and G. Gentili and I. Sabadini and D. C. Struppa},
journal= {arXiv preprint arXiv:0708.3592},
year = {2015}
}