An Overview on Functional Calculus in Different Settings
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.
KeywordsFunctional 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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