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Lecture Notes on C-algebras - UVic.ca

Lecture Notes onC -algebrasIan F. PutnamJanuary 3, 20192 Contents1 Basics ofC Definition .. Examples .. Spectrum .. CommutativeC -algebras .. Further consequences of theC -condition .. Positivity .. Finite-dimensionalC -algebras .. Non-unitalC -algebras .. Ideals and quotients .. Traces .. Representations .. The GNS construction .. von Neumann algebras .. 602 GroupC Group representations .. Group algebras .. Finite groups .. TheC - algebra of a discrete group .. Abelian groups .. The infinite dihedral group .. The groupF2.. Locally compact groups .. 913 GroupoidC Groupoids .. Topological groupoids .. TheC - algebra of an etale groupoid.

8 CHAPTER 1. BASICS OF C-ALGEBRAS Very simply, Ahas an algebraic structure and a topological structure coming from a norm. The condition that Abe a Banach algebra expresses

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