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Introduction

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

Abstract

Since the discovery of the S-spectrum in 2006 the theory of slice hyperholomorphic functions has become the underlining function theory on which new functional calculi for quaternionic operators and for n-tuples of operators have been developed. These calculi are the S-functional calculus and the F-functional calculus, and both are based on the notion of S-spectrum. In 2014 it was proved that the quaternionic spectral theorem is also naturally based on the S-spectrum. These facts restore the analogy with the classical case in which the holomorphic functional calculus and the spectral theorem are based on the same notion of spectrum.

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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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