Normal operators in real and quaternionic Hilbert spaces

2021/03/30 by Vasilescu, Florian-Horia
#47A60 #47S05 #FOS: Mathematics #Functional Analysis (math.FA) #Subject Classification 2020: 47B15

paper · doi:10.48550/arxiv.2103.16266

Abstract

A new approach to normal operators in real Hilbert spaces is discussed, and a spectral representation is obtained, derived directly from the complex case. The results are then applied to quaternionic normal operators, regarded as a special class of real normal operators. This point of view allows us to consider their spectrum and associated measures to be defined on subsets of the complex plane, in a classical manner.

Related

• Spectral theorem for unbounded normal operators in quaternionic Hilbert spaces
• Spectral properties of compact normal quaternionic operators
• Spectral Theorem for quaternionic normal operators: Multiplication form
• The Spectral Theorem for Quaternionic Normal Operators
• S-spectrum and numerical range of a quaternionic operator