# Spectral properties of compact normal quaternionic operators

February 12, 2014

General, especially spectral, features of compact normal operators in
quaternionic Hilbert spaces are studied and some results are established which
generalize well-known properties of compact normal operators in complex Hilbert
spaces. More precisely, it is proved that the norm of such an operator always
coincides with the maximum of the set of absolute values of the eigenvalues
(exploiting the notion of spherical eigenvalue). Moreover the structure of the
spectral decomposition of a generic compact normal operator $T$ is discussed
also proving a spectral characterization theorem for compact normal operators.

open access link
Hypercomplex Analysis: New perspectives and applications, Trends in Mathematics, Birkhauser, Basel (2014)

Keywords:

quaternionic functional analysis, compact operators