Published February 15, 1994
| Version public
Journal Article
The Index of a Pair of Projections
Creators
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1.
Technion – Israel Institute of Technology
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2.
Technical University of Berlin
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.
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.Additional details
Identifiers
- Eprint ID
- 81208
- Resolver ID
- CaltechAUTHORS:20170906-144540972
Funding
- NSF
- DMS-9101715
- German-Israeli Foundation for Research and Development
Dates
- Created
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2017-09-06Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
Caltech Custom Metadata
- Caltech groups
- Mathematics Department , Physics Department