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Spectral Integrals

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

Abstract

In this chapter, we define spectral integrals in the quaternionic setting. The aim is to de_ne them for a suitably large class of functions that allows us to prove the spectral theorem for unbounded operators in Section 12. To this end, we adapt part of Chapter 4 of the book [191] to the quaternionic setting. Most of the proofs of the properties of spectral integrals are easily adapted from the classical case presented in [191], i.e., when H is a complex Hilbert space. However, some facts require additional arguments, which we will highlight.

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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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