On the index of meromorphic operator-valued functions and some applications

Abstract

We revisit and connect several notions of algebraic multiplicities of zeros of analytic operator-valued functions and discuss the concept of the index of meromorphic operator-valued functions in complex, separable Hilbert spaces. Applications to abstract perturbation theory and associated Birman-Schwinger-type operators and to the operator-valued Weyl-Titchmarsh functions associated to closed extensions of dual pairs of closed operators are provided.

24 pages, some corrections and updates were made. This paper revisits and extends some parts of arXiv:1405.4910