Abstract
Let X be a two-sided quaternionic Banach space and let \(A, B, C: X \longrightarrow X\) be bounded right linear quaternionic operators such that \(ACA=ABA\). Let q be a non-zero quaternion. In this paper, we investigate the common properties of \((AC)^{2}-2Re(q)AC+|q|^2I\) and \((BA)^{2}-2Re(q)BA+|q|^2I\) where I stands for the identity operator on X. In particular, we show that
where \(\sigma ^{S}_{{\mathcal {F}}}(.)\) is a distinguished part of the spherical spectrum.
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Communicated by Fabrizio Colombo.
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Arzini, R., Jaatit, A. Common Spectral Properties of Bounded Right Linear Operators AC and BA in the Quaternionic Setting. Adv. Appl. Clifford Algebras 34, 11 (2024). https://doi.org/10.1007/s00006-024-01315-0
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DOI: https://doi.org/10.1007/s00006-024-01315-0