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On the index of meromorphic operator-valued functions and some applications. (English) Zbl 1441.47012

Dittrich, Jaroslav (ed.) et al., Functional analysis and operator theory for quantum physics. The Pavel Exner anniversary volume. Dedicated to Pavel Exner on the occasion of his 70th birthday. Zürich: European Mathematical Society (EMS). EMS Ser. Congr. Rep., 95-127 (2017).
The aim of this paper, dedicated to Pavel Exner on the occasion of his 70th birthday, is multifold. The authors revisit some recent results on factorizations of analytic operator-valued Fredholm functions and apply this to algebraic multiplicities of bounded, analytic operator-valued Fredholm functions. Hereafter they discuss the notion of an index of meromorphic operator-valued functions. The previous results are applied to Birman-Schwinger operators in connection with abstract perturbation theory and to operator-valued Weyl-Titchmarsh functions associated to closed extensions of dual pairs of closed operators.
For the entire collection see [Zbl 1364.46005].

MSC:

47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
47A53 (Semi-) Fredholm operators; index theories
47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
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