Quasi-permutable normal operators in octonion Hilbert spaces and spectra

TL;DR

This paper explores the properties and spectra of quasi-permutable normal operators in octonion Hilbert spaces, introduces multiparameter semigroups of these operators, and proves a non-associative version of Stone's theorem.

Contribution

It provides new insights into the spectral theory of non-associative operators and extends classical results like Stone's theorem to octonion Hilbert spaces.

Findings

Spectra of quasi-permutable normal operators are characterized.

Multiparameter semigroups of such operators are constructed.

A non-associative analog of Stone's theorem is established.

Abstract

Families of quasi-permutable normal operators in octonion Hilbert spaces are investigated. Their spectra are studied. Multiparameter semigroups of such operators are considered. A non-associative analog of Stone's theorem is proved.