Abstract:

We provide a genealogy or conceptual history of p-adic triangular Banach algebras (TUHF) and p-adic UHF Banach algebras (UHF). We describe how, by replacing the field C of complex numbers by the universal p-adic field Ω_p, the concept of a complex UHF C∗-algebra evolved directly into the concept of p-adic triangular (TUHF) Banach algebras and the concept of p-adic UHF algebras.