Characterization of Subnormal Operators in C*-algebra

Abstract

The study investigates subnormal operators in C*-algebras, addressing unresolved challenges in their characterization. This research aims to provide a clear algebraic framework for subnormal operators, utilizing matrix representations to explain their properties of normality, subnormality, self-adjointness, and isometry. The specific objectives include stating the algebraic characterization of subnormal operators, offering concise characterizations of C*-algebra elements, and establishing results from operator theory that highlight the invertibility and other critical properties of these elements. Grounded on Muhly and Solel, Rørdam and Williams theorem, the methodology involves a theoretical analysis of subnormal operators in Hilbert spaces and their relationships with C*-algebras. The research findings successfully achieve the set objectives, presenting a detailed algebraic characterization of subnormal operators and elucidating their role within C*-algebras. The conditions for subnormality were effectively applied, improving the understanding of the structure and dynamics of these algebras.