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An Overview on Functional Calculus in Different Settings

  • Fabrizio Colombo
  • Graziano Gentili
  • Irene Sabadini
  • Daniele C. Struppa
Part of the Trends in Mathematics book series (TM)

Abstract

In this paper we give an overview of some different versions of functional calculus in a noncommutative setting. In particular, we will focus on a recent functional calculus based on the notion of slice-hyperholomorphy. This notion, in suitable versions, will allow us to study the case of linear quaternionic operators, as well as the case of n-tuples of linear (real or complex) operators.

Keywords

Functional calculus spectral theory bounded and unbounded operators linear quaternionic operators n-tuples of linear operators 

Mathematics Subject Classification (2000)

Primary 47A10, 30G35 Secondary 47A60 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Fabrizio Colombo
    • 1
  • Graziano Gentili
    • 2
  • Irene Sabadini
    • 1
  • Daniele C. Struppa
    • 3
  1. 1.Department of Mathematics and Computer SciencesChapman UniversityOrangeUSA
  2. 2.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  3. 3.Dipartimento di MatematicaUniversitá di FirenzeFirenzeItaly

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