Abstract
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.
Mathematics Subject Classification (2010).46S10, 47C15, 47B07, 30G35, 81R15.
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© 2014 Springer International Publishing Switzerland
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Ghiloni, R., Moretti, V., Perotti, A. (2014). Spectral Properties of Compact Normal Quaternionic Operators. In: Bernstein, S., Kähler, U., Sabadini, I., Sommen, F. (eds) Hypercomplex Analysis: New Perspectives and Applications. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-08771-9_9
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DOI: https://doi.org/10.1007/978-3-319-08771-9_9
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-08770-2
Online ISBN: 978-3-319-08771-9
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