Continuous Slice Functional Calculus in Quaternionic Hilbert Spaces

@inproceedings{Ghiloni2013ContinuousSF,
  title={Continuous Slice Functional Calculus in Quaternionic Hilbert Spaces},
  author={Riccardo Ghiloni and Valter Moretti and Alessandro Perotti},
  year={2013}
}
The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest, the class of continuous functions to consider in this setting is the one of slice quaternionic functions. Slice functions generalize the concept of slice regular function, which comprises power series with quaternionic coefficients on one side and that can be… CONTINUE READING