Decomposable operators, local S-spectrum and S-spectrum in the quaternionic setting

2019/05/15 by Thirulogasanthar, K., Muraleetharan, B.
#47A53 #47B07 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47A10 #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1905.05936

Abstract

In a right quaternionic Hilbert space, following the complex formalism, decomposable operators, the so-called Bishop's property and the single valued extension property are defined and the connections between them are studied to certain extent. In particular, for a decomposable operator, it is shown that the S-spectrum, approximate S-point spectrum, surjectivity S-spectrum and the union of all local S-spectra coincide. Using continuous right slice-regular functions we have also studied certain properties of local S-spectrum and local S-spectral subspaces.

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