Non commutative functional calculus: unbounded operators
Abstract
In a recent work, cgss, we developed a functional calculus for bounded operators defined on quaternionic Banach spaces. In this paper we show how the results from 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.
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