Notes on $C^{*}$-algebras

TL;DR

This paper provides comprehensive lecture notes on $C^{*}$-algebras, covering fundamental theorems, constructions, and advanced topics like K-theory, aimed at graduate-level understanding.

Contribution

It offers an organized exposition of key concepts and recent developments in $C^{*}$-algebra theory for educational purposes.

Findings

Clarifies Gelfand-Naimark theorems

Explains universal C*-algebras and Hilbert C*-modules

Discusses crossed products, Morita equivalence, and K-theory

Abstract

These lecture notes on $C^{*}$-algebras were prepared for a couple of courses given by the author at IMSc and also at IIT Gandhinagar. The topics covered are: Gelfand-Naimark theorems, universal C*-algebras, Hilbert C*-modules, crossed products, Morita equivalence, K-theory.