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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Triangular truncation and normal limits of nilpotent operators
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by Don Hadwin PDF
Proc. Amer. Math. Soc. 123 (1995), 1741-1745 Request permission

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
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1741-1745
  • MSC: Primary 47A58; Secondary 15A60, 47A30, 47A65
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1257109-0
  • MathSciNet review: 1257109