Borel functional calculus for quaternionic normal operators

摘要

In this article, we give an approach to Borel functional calculus for quaternionic normal operators, which are not necessarily bounded. First, we establish the definition of functional calculus for a subclass of quaternion valued Borel functions, and then we extend the same to the class of quaternion valued Borel functions as well as L-infinity-functions. We also prove spectral mapping theorem as a consequence. Published by AIP Publishing.