In this paper we announce the development of a functional calculus for operators defined on quaternionic Banach spaces. The definition is based on a new notion of slice regularity, see , and the key tools are a new resolvent operator and a new eigenvalue problem. This approach allows us to deal both with bounded and unbounded operators.
Colombo, F., Gentili, G., Sabadini, I., Struppa, D.C.: A functional calculus in a non commutative setting. Electronic Research Announcements in Mathematical Sciences 14, 60–68 (2007). Retrieved from http://www.aimsciences.org/journals/pdfsnews.jsp?paperID=2888&mode=full
American Institute of Mathematical Sciences