01-298 Marius Mantoiu

C*-Algebras, Dynamical Systems at Infinity and the Essential Spectrum of Generalized Schrodinger Operators (540K, ps) Aug 7, 01

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Abstract. We introduce classes of C*-algebras to which anisotropic Schrodinger operators are affiliated. In an abstract framework, we study decompositions of the quotients of these C*-algebras by the ideal of compact operators. These are induced by invariant decompositions of a dynamical system "at infinity" defined by the class of potentials we consider. As a consequence, we get formulae for the essential spectrum of the affiliated anisotropic operators. The theory is illustrated by two types of examples which do not seem to be accessible to standard methods (as Weyl sequences).

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