Pseudo differential operators with operator-valued symbols

Pseudodifferential calculus on manifolds with edges in the form developed by B-W. Schulze is organised locally as Fourier calculus along the edges with symbols acting as operators in the transversal cone spaces. Thus, the index problem in the wedge algebra can be treated within a general framework of pseudodifferential operators with operator-valued symbols. In this paper, we introduce a concept of ellipticity for such operators and prove an index formula for elliptic elements.