2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152319This is a survey of four recent papers which deal with the relationship of simple C*-algebras to the problem of computing the spectra of self-adjoint operators in the general case, especially when the spectrum is not discrete. It is an expanded version of a talk presented at the 50 year C*-algebra celebration, held at the annual meeting of the AMS in San Antonio during January, 1993.14 pages, AMS-TeX 2.1Functional AnalysisOperator Algebrastext