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Published February 15, 1994 | metadata_only
Journal Article

The Index of a Pair of Projections


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.

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August 20, 2023
August 20, 2023