English

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.

Keywords

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

R2 v1 2026-06-23T09:06:52.108Z