Non commutative functional calculus: unbounded operators

Details Non commutative functional calculus: unbounded operators Non commutative functional calculus: unbounded operators

2007-08-27

arxiv.org/abs/0708.3592v2

J. Geom. Phys. 60 (2010), 251-259

Mathematics

Spectral Theory

Scientific paper

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.

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