A C^{{star operator}} algebra of pseudodifferential operators on the half line

Abstract

In this paper we employ a C{star operator}-algebra approach to the study of Fredholm properties of differential and pseudodifferential operators on the half line. The algebra investigated in this paper has compact commutators, so the Gelfand theory applies to the quotient algebra, and we obtain an explicit description of the corresponding maximal ideal space and necessary and sufficient conditions for Fredholmness of operators in the algebra. © 2014 Elsevier Inc.