Remarks on Holomorphic Families of Schrödinger and Dirac Operators

Abstract

Holomorphic families T(κ) = T + κA of linear operators in a Hilbert space are considered, where T and A are m-accretive. Detailed results are given when A is positive selfadjoint. We are interested in the case in which T(κ) forms a family of type (A) for κ in a region of the complex plane and of a weaker type (say type (B)) in a larger region. Dirac and Schrodinger operators with singular potentials are discussed. The abstract part consists of two theorems which generalize a theorem of H. Sohr.