Infinite sum relations on universal C*-algebras

• DOI: 10.1016/j.jmaa.2021.125850
• Publication Date: 2021-11-22T16:30:38Z
• Authors: Giuliano Boava; Gilles G. de Castro
• Keywords: Operator algebra; Operator (biology)

We extend the usual theory of universal C*-algebras from generators and relations in order to allow some relations to be described using the strong operator topology. In particular, we can allow some infinite sum relations. We prove a universal property for the algebras we define and we show how the Cuntz algebra of infinite isometries as well as the Exel-Laca algebras can be described using infinite sum relations. Finally, we give some sufficient conditions for when a C*-algebra generated by projections and partial isometries is a universal C*-algebra using only norm relations, in case one still wants to avoid using relations with respect to the strong operator topology.