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The Index of a Pair of Projections

Avron, J. and Seiler, R. and Simon, B. (1994) The Index of a Pair of Projections. Journal of Functional Analysis, 120 (1). pp. 220-237. ISSN 0022-1236. https://resolver.caltech.edu/CaltechAUTHORS:20170906-144540972

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Abstract

We discuss pairs of self-adjoint projections with P − Q ∈ J_(2n + 1), the trace ideal, and prove that for m ≥ n, tr(P − Q)^(2m + 1) = tr(P − Q)^(2n + 1) = dim(Ker Q ∩ Ran P) − dim(Ker P ∩ Ran Q) is an integer. We also prove that there exists a unitary V interchanging P and Q if and only if this integer is 0.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1006/jfan.1994.1031DOIArticle
http://www.sciencedirect.com/science/article/pii/S0022123684710317PublisherArticle
ORCID:
AuthorORCID
Simon, B.0000-0003-2561-8539
Additional Information:© 1994 Academic Press. Received March 1, 1993. Communicated by L. Gross. Research partially supported by US NSF Grant DMS-9101715. We thank M. Ben-Artzi for the hospitality of Hebrew University where some of this work was done and I. Kaplansky for a useful question. The research is partially supported by GIF.
Funders:
Funding AgencyGrant Number
NSFDMS-9101715
German-Israeli Foundation for Research and DevelopmentUNSPECIFIED
Issue or Number:1
Record Number:CaltechAUTHORS:20170906-144540972
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170906-144540972
Official Citation:J. Avron, R. Seiler, B. Simon, The Index of a Pair of Projections, Journal of Functional Analysis, Volume 120, Issue 1, 1994, Pages 220-237, ISSN 0022-1236, http://dx.doi.org/10.1006/jfan.1994.1031. (http://www.sciencedirect.com/science/article/pii/S0022123684710317)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81208
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:06 Sep 2017 22:02
Last Modified:03 Oct 2019 18:40

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