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A characterization of thin operators in a von Neumann algebra
1973
Proceedings of the American Mathematical Society
Let si be a von Neumann algebra, J a uniformly closed, weakly dense, two-sided ideal in si, S the center of si', and 9 the lattice of projections in J. An operator A e si is thin relative to J if A =Z+K, for some Ze2C,KeJ. The thin operators relative to J are characterized as those A es/ satisfying \\mpv?\\AP-PA\\=0. It is also shown that lim sup \\PAP -AP\\ = lim sup \\PAP -PA\\. Pe& PeSP 1. Let si be a von Neumann algebra, «/ a uniformly closed, weakly dense, two-sided ideal in si, 2£ the
doi:10.1090/s0002-9939-1973-0341121-5
fatcat:kzysobhqt5erzpmto5wpv7rr6y