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Spectral Flows of Dilations of Fredholm Operators

Published online by Cambridge University Press:  20 November 2018

Giuseppe De Nittis  and
Hermann Schulz-Baldes
Giuseppe De Nittis
Affiliation:
Department Mathematik, Universit¨at Erlangen-Nürnberg, Germany. e-mail: denittis@math.fau.de, e-mail: schuba@mi.uni-erlangen.de
Hermann Schulz-Baldes
Affiliation:
Department Mathematik, Universit¨at Erlangen-Nürnberg, Germany. e-mail: denittis@math.fau.de, e-mail: schuba@mi.uni-erlangen.de
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Abstract

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Given an essentially unitary contraction and an arbitrary unitary dilation of it, there is a naturally associated spectral flow that 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 Z2 indices of odd symmetric Fredholm operators to a Z2-valued spectral flow.

Keywords

19K5646L80spectral flowFredholm operatorsZ2 indices
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 1 , 01 March 2015 , pp. 51 - 68
Copyright
Copyright © Canadian Mathematical Society 2015

References

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