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Measurable enumeration of eigenelements

Gordon, Alexander Y. and Kechris, Alexander S. (1998) Measurable enumeration of eigenelements. Applicable Analysis: An International Journal, 71 (1-4). pp. 41-61. ISSN 0003-6811. http://resolver.caltech.edu/CaltechAUTHORS:20130528-105907286

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Abstract

We prove that for eigenelements of a measurable family of linear self-adjoint operators in a separable Hilbert space there exists a measurable enumeration. We also prove a similar result for measurable families of bounded linear operators having at most countably many eigenvalues (under certain restrictions on the parameter space). The proof of the latter result is based on descriptive set theory, while in the case of self-adjoint (and some more general) operators the proof is constructive.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://www.tandfonline.com/doi/abs/10.1080/00036819908840704#.UaTxYPKYl8EPublisherUNSPECIFIED
Additional Information:© 1999 OPA (Overseas Publishers Association) N. V. Published by license under the Gordon and Breach Science Publishers imprint. Received: 5 1998; Published online: 20 Jan 2011. Research partially supported by NSF Grant DMS 96-19880. We are indebted to S. Jitomirskaya, Y. Last, C. Remling, and B. Simon for useful discussions. The first named author is grateful for the hospitality of the Division of Physics, Mathematics and Astronomy of Caltech and the Department of Mathematics of the University of California at Irvine, where parts of this work were done.
Funders:
Funding AgencyGrant Number
NSFDMS 96-19880
Subject Keywords:Measurable space; eigenvalue; eigenvector; measurable enumeration
Other Numbering System:
Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR1690090
Classification Code:AMS: 47A56, 26E25, 54C65, 28B20
Record Number:CaltechAUTHORS:20130528-105907286
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20130528-105907286
Official Citation:Measurable enumeration of eigenelements Alexander Y. Gordon, Alexander S. Kechris Applicable Analysis Vol. 71, Iss. 1-4, 1998
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38691
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:28 May 2013 23:05
Last Modified:28 May 2013 23:08

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