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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stability of semi-Fredholm properties in complex interpolation spaces


Authors: Karl-Heinz Förster and Kerstin Günther
Journal: Proc. Amer. Math. Soc. 139 (2011), 3561-3571
MSC (2000): Primary 46B70, 47A53, 47A55
Published electronically: March 29, 2011
MathSciNet review: 2813387
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Abstract: In this paper, we show that for interpolation morphisms $ \vec{S}$ and the complex interpolation method the set of all $ \theta\in(0,1)$ such that $ S_{[\theta]}$ is a semi-Fredholm operator is open and the nullities, deficiencies and the indices of $ S_{[\theta]}$ are locally constant on this set.


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Additional Information

Karl-Heinz Förster
Affiliation: Technische Universität Berlin, MA 6-4, Strasse des 17. Juni 136, 10623 Berlin, Germany
Email: foerster@math.tu-berlin.de

Kerstin Günther
Affiliation: Technische Universität Berlin, MA 6-4, Strasse des 17. Juni 136, 10623 Berlin, Germany
Email: guenther@math.tu-berlin.de

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10761-5
PII: S 0002-9939(2011)10761-5
Keywords: Interpolation theory, complex interpolation method, duality, Fredholm operators, Punctured Neighborhood Theorem
Received by editor(s): February 27, 2009
Received by editor(s) in revised form: May 27, 2010, and August 25, 2010
Published electronically: March 29, 2011
Additional Notes: The authors thank the referee for helpful suggestions which improved the presentation of the paper.
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.