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Proceedings of the American Mathematical Society

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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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  • [ACN] J. R. Angelos, C. C. Cowen, and S. K. Narayan, Triangular truncation and finding the norm of a Hadamard multiplier, Linear Algebra Appl. 170 (1992), 117-135. MR 1160957 (93d:15039)
  • [AFHV] C. Apostol, L. Fialkow, D. Herrero, and D. Voiculescu, Approximation of Hilbert space operators, Vol. II, Pitman, Boston, 1984. MR 735080 (85m:47002)
  • [AFV] C. Apostol, C. Foias, and D. Voiculescu, Norm limits of nilpotents, II, Rev. Roumaine Math. Pures Appl. 19 (1974), 549-577. MR 0417828 (54:5876)
  • [D] K. Davidson, Nest algebras, Pitman Res. Notes Math. Ser., no. 191, Longman Sci. Tech., Harlow, 1988. MR 972978 (90f:47062)
  • [H1] D. A. Herrero, Normal limits of nilpotents operators, Indiana Univ. Math. J. 23 (1974), 1097-1108. MR 0350476 (50:2968)
  • [H2] -, Approximation of Hilbert space operators. I, Research Notes in Math., vol. 72, Pitman, Boston, 1982.
  • [K] W. Kahan, Every $ n \times n$ matrix Z with real spectrum satisfies $ \left\Vert {Z - {Z^ \ast }} \right\Vert \leq \left\Vert {Z + {Z^ \ast }} \right\Vert\{ {\log _2}n + 0.038\} $, Proc. Amer. Math. Soc. 39 (1973), 235-241. MR 0313278 (47:1833)
  • [KP] S. Kwapien and A. Pelczynski, The main triangle projection in matrix spaces and its application, Studia Math. 34 (1970), 43-68. MR 0270118 (42:5011)

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Article copyright: © Copyright 1995 American Mathematical Society

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