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# Spectral Flows of Dilations of Fredholm Operators

Published:2014-11-19
Printed: Mar 2015
• Giuseppe De Nitties,
Department Mathematik, Universität Erlangen-Nürnberg, Germany
• Hermann Schulz-Baldes,
Department Mathematik, Universität Erlangen-Nürnberg, Germany
 Format: LaTeX MathJax PDF

## 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 result is interpreted in terms of the $K$-theory of an associated mapping cone. It is then extended to connect $\mathbb{Z}_2$ indices of odd symmetric Fredholm operators to a $\mathbb{Z}_2$-valued spectral flow.
 Keywords: spectral flow, Fredholm operators, Z2 indices
 MSC Classifications: 19K56 - Index theory [See also 58J20, 58J22] 46L80 - $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]

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