Abstract
This chapter discusses ideals and positive functional. Every C*-algebra can be realized as a C*-subalgebra of B (H) for some Hilbert space H. This is the Gelfand–Naimark theorem, and it is one of the fundamental results of the theory of C*-algebras. A key step in its proof is the GNS construction that sets up a correspondence between the positive linear functionals and some of the representations of the algebra. There are also deep connections between the positive linear functionals and the closed ideals and closed left ideals of the algebra. The chapter also discusses the hereditary C*-sub-algebras. These are a sort of generalizations of ideals and are of great importance in the theory. It also presents the application of some of the results developed to an interesting and highly non-trivial class of operators, the Toeplitz operators.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
