Decomposable operators, local S-spectrum and S-spectrum in the quaternionic setting
Functional Analysis
2019-05-17 v1 Spectral Theory
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.
Cite
@article{arxiv.1905.05936,
title = {Decomposable operators, local S-spectrum and S-spectrum in the quaternionic setting},
author = {K. Thirulogasanthar and B. Muraleetharan},
journal= {arXiv preprint arXiv:1905.05936},
year = {2019}
}
Comments
28 pages. arXiv admin note: text overlap with arXiv:1904.02977