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

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