C* Algebras and Representation

Bhura, Omkar (2022) C* Algebras and Representation. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Omkar BHhura (17MS125 )) 17MS125_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (894kB)

Abstract

In this project, we study Gelfand–Naimark–Segal construction of cyclic representation from a positive linear functional on a C*-algebra which in turn says that any C⇤-algebra is isometrically isomorphic to some C*-subalgebra of B(H) for some Hilbert space H. We also studied the theory of spectral measure to study the spectral theory of normal operators to have an analogous representation of normal operator as in case of finite dimension except that the finite sum get replaced by integration with respect spectral measure. Along the way, in order to study these, we have learnt various topics that includes Banach algebra, spectrum, maximal ideal space, Gelfand transform, Riesz functional calculus, C*-Algebra, Ideal and quotients, continuous functional calculus, states and pure states, representation of C*-Algebras, spectral measures, and L1-functional calculus.

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