B*-algebras over ultranormed fields

TL;DR

This paper explores the structure and properties of B*-algebras over ultranormed fields, including their radicals, extensions, and connections to operator theory, advancing the theoretical understanding of these algebraic systems.

Contribution

It provides a detailed structural analysis of B*-algebras over ultranormed fields, including radicals, extensions, and their relations to operator algebras, which is a novel theoretical contribution.

Findings

Characterization of B*-algebras over ultranormed fields

Investigation of radicals and core radicals in these algebras

Connections established between B*-algebras and operator theory

Abstract

This article is devoted to the investigation of $B^*$-algebras, dual and annihilator ultranormed algebras. Their structure is studied in the paper. Extensions of algebras and fields are considered and using them core radicals and radicals are investigated. Moreover, for this purpose also $*$-algebras and finely regular algebras are studied. Relations with operator theory and realizations of these algebras by operator algebras are outlined.