On the index of meromorphic operator-valued functions and some applications
Jussi BehrndtTU Graz, Austria
Fritz GesztesyBaylor University, Waco, USA
Helge HoldenUniversity of Trondheim, Norway
Roger NicholsThe University of Tennessee at Chattanooga, USA
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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.