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arXiv · 1405.0410

Spectral flows of dilations of Fredholm operators

Giuseppe De Nittis·Hermann Schulz-Baldes
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Abstract

Given an essentially unitary contraction and an arbitrary unitary dilation of it, there is a naturally associated spectral flow which is shown to be equal to the index of the operator. This purely operator theoretic result is interpreted in terms of the $K$-theory of an associated mapping cone. It is then extended to connect $Z_2$ indices of odd symmetric Fredholm operators to a $Z_2$-valued spectral flow.

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Giuseppe De Nittis, Hermann Schulz-Baldes. 2015-02-27. Spectral flows of dilations of Fredholm operators. https://doi.org/10.4153/cmb-2014-055-3

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