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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
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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 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 spectral flow, Fredholm operators, Z2 indices
MSC Classifications: 19K56, 46L80 show english descriptions Index theory [See also 58J20, 58J22]
$K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
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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