C*-algebras associated with some second order differential operators

Abstract

We compare two C*-algebras that have been used to study the essential spectrum. This is done by considering a simple second order elliptic differential operator acting in L^2(R^N), which is affiliated with one or both of the algebras depending on the behaviour of the coefficients.

16 pages, second and final version. Key words: spectral analysis, essential spectrum, C*-algebras, elliptic differential operators