Riesz projection and essential S-spectrum in quaternionic setting

2021/08/02 by Hatem Baloudi, Baloudi, Hatem, Sayda Belgacem +3 · 1 citation
Mathematics · #Algebraic and Geometric Analysis #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2108.01157

openalex publication_date 2021/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to the investigation of the Weyl and the essential S-spectrum of a bounded right quaternionic linear operator in a right quaternionic Hilbert space. Using the quaternionic Riesz projection, the S-eigenvalue of finite type is introduced and studied. In particular, it is shown that the Weyl and the essential S-spectra does not contains eigenvalues of finite type. We also describe the boundary of the Weyl S-spectrum and the particular case of the spectral theorem of the essential S-spectrum.

Cited by

• Local Rigidity of Quasi--Lie Brackets on Quaternionic Banach Modules and Applications to Nonlinear PDEs

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