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The S-Spectrum and the S-Functional Calculus

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

Abstract

The fundamental difficulty in developing a mathematically rigorous theory of quaternionic linear operators was the identification of suitable notions of quaternionic spectrum and quaternionic resolvent operator. In this chapter we study the properties of the S-spectrum and the S-resolvent operators, and we introduce the quaternionic S-functional calculus.

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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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