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The S-Functional Calculus for Unbounded Operators

  • Fabrizio Colombo
  • Jonathan Gantner
  • David P. Kimsey
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 270)

Abstract

The S-functional calculus can also be defined for unbounded operators. We consider a two-sided quaternionic Banach space X and we introduce a notation for the set of unbounded operators that we consider in this chapter. These results are taken from the papers [67,97], where we reduce the case of unbounded operators, with suitable transformations, to the case of bounded operators. The direct approach has been studied in the more recent paper [124], while the S-resolvent equation is in [50].

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Fabrizio Colombo
    • 1
  • Jonathan Gantner
    • 1
  • David P. Kimsey
    • 2
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2.School of Mathematics, Statistics & PhysicsNewcastle UniversityNewcastle upon TyneUK

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