A theorem of Calderh-Vaillancourt type is obtained for a class of pseudodifferential IpLrbtors with operator -valued symbols, and strongly continuous (in general nonsmooth) groups # lrornorphisms involved in the symbol estimates.
The theory of pseudodifferential operators on singular manifolds, i. e., manifolds with #Ingular geometries in the sense of piecewise smooth Riemannian metrics, has seen a hitful developement throughout the past decades. In particular, pseudodifferential Qperators on compact manifolds with conical singularities, edges, and corners were Intensively studied. In this connection we want to mention the works of MELROSE
IlO], PLAMENEVSKIJ [13], SCHULZE [17], [19],
[20], and their coworkers.
Less attention is paid to the case of non-compact singular manifolds. Indeed, the lioncompactness of an underlying configuration may be viewed as a further kind of Ilngularity, whose treatment requires a precise control of the operators "at infinity". The analysis of non -compact manifolds is not only interesting in its own right, but even arises naturally in calculi on compact singular manifolds, where the ellipticity of pseudodifferential operators typically is described via principal symbols that take values in operator algebras on "less singular", but noncompact objects. Such an tffect already appears for boundary value problems, where the Shapiro -Lopatinskij condition requires bijectivity of the boundary symbol, which is a family of operators on the normal to the boundary, i. e., on the real half-axis.
The present paper provides general material to handle manifolds with noncompact edges. We therefore combine elements of S CHULZE'S calculi for singular manifolds and classical techniques of the analysis of global pseudodifferential operators on a Euclidean apace, as they were introduced by CORDES [l], PARENTI [ll], and SHUBIN [23], and extended to so-called SG-manifolds by SCHROHE [15]. The local model of a manifold with edge is a wedge, i.e., a Cartesian product of a