Non-commutative Functional Calculus: Unbounded Operators
In a recent work, Colombo (in press), we developed a functional calculus for bounded operators defined on quaternionic Banach spaces. In this paper we show how the results from the above-mentioned work 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.
Colombo, F., Gentili, G., Sabadini, I., & Struppa, D. C. (2010). Non-commutative functional calculus: Unbounded operators. Journal of Geometry and Physics, 60(2), 251-259. doi: 10.1016/j.geomphys.2009.09.011