Notes on universal C*-algebras

Abstract

In these notes, we explain in details the construction of the universal C*-algebra as done by Blackadar, starting with the construction of the free *-algebra. At the end, we explain the extension done by Boava and the author to include relations described using the strong operator topology. As an example, we show that a graph C*-algebra can be defined using infinite sums.

Notes for three lectures given at IMPAN in 2023 part of the Banach Center Simons Semester Operator Algebras That One Can See