Spectral properties of compact normal quaternionic operators

2014/02/12 by Riccardo Ghiloni, Valter Moretti, Ghiloni, Riccardo +3 · 1 citation
Mathematics · #Algebraic and Geometric Analysis #Spectral Theory in Mathematical Physics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1402.2935

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.

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• Octonionic Para-linear Self-Adjoint Operators and Spectral Decomposition

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