Non commutative functional calculus: unbounded operators

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.

References in corpus (3)

• A new functional calculus for non-commuting operators
• Poles of regular quaternionic functions
• Non commutative functional calculus: bounded operators

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• Pontryagin de Branges Rovnyak spaces of slice hyperholomorphic functions
• Berberian extension and its S-spectra in a quaternionic Hilbert space
• Decomposable operators, local S-spectrum and S-spectrum in the quaternionic setting
• Schur functions and their realizations in the slice hyperholomorphic setting