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Triangular truncation and normal limits of nilpotent operators

1995
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Proceedings of the American Mathematical Society
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We show that, as n -» oo , the product of the norm of the triangular truncation map on the n x n complex matrices with the distance from the normone hermitian «x« matrices to the nilpotents converges to 1/2. We also include an elementary proof of D. Herrero's characterization of the normal operators that are norm limits of nilpotents. Suppose zz is a positive integer and let Jin , ETn , jVn denote, respectively, the sets of all zz x zz complex matrices, strictly upper triangular zz x zz

doi:10.1090/s0002-9939-1995-1257109-0
fatcat:qmktrzqipvcnhcz5x7tq5chll4