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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Triangular truncation and normal limits of nilpotent operators


Author: Don Hadwin
Journal: Proc. Amer. Math. Soc. 123 (1995), 1741-1745
MSC: Primary 47A58; Secondary 15A60, 47A30, 47A65
MathSciNet review: 1257109
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Abstract: We show that, as $ n \to \infty $, the product of the norm of the triangular truncation map on the $ n \times n$ complex matrices with the distance from the norm-one hermitian $ n \times n$ 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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1257109-0
PII: S 0002-9939(1995)1257109-0
Article copyright: © Copyright 1995 American Mathematical Society