Berberian extension and its S-spectra in a quaternionic Hilbert space

2019/11/17 by Muraleetharan, B., Thirulogasanthar, K.
#47A10 #47B47 #47L05 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1911.08561

Abstract

For a bounded right linear operators A, in a right quaternionic Hilbert space V_ℍ^R, following the complex formalism, we study the Berberian extension A^∘, which is an extension of A in a right quaternionic Hilbert space obtained from V_ℍ^R. In the complex setting, the important feature of the Berberian extension is that it converts approximate point spectrum of A into point spectrum of A^∘. We show that the same is true for the quaternionic S-spectrum. As in the complex case, we use the Berberian extension to study some properties of the commutator of two quaternionic bounded right linear operators.

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