Triangular truncation and normal limits of nilpotent operators
Author:
Don Hadwin
Journal:
Proc. Amer. Math. Soc. 123 (1995), 17411745
MSC:
Primary 47A58; Secondary 15A60, 47A30, 47A65
MathSciNet review:
1257109
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Abstract: We show that, as , the product of the norm of the triangular truncation map on the complex matrices with the distance from the normone hermitian 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.
 [ACN]
James
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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), 117135. 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), 549577. 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), 10971108. MR 0350476 (50:2968)
 [H2]
 , Approximation of Hilbert space operators. I, Research Notes in Math., vol. 72, Pitman, Boston, 1982.
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 W. Kahan, Every matrix Z with real spectrum satisfies , Proc. Amer. Math. Soc. 39 (1973), 235241. MR 0313278 (47:1833)
 [KP]
 S. Kwapien and A. Pelczynski, The main triangle projection in matrix spaces and its application, Studia Math. 34 (1970), 4368. MR 0270118 (42:5011)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199512571090
PII:
S 00029939(1995)12571090
Article copyright:
© Copyright 1995
American Mathematical Society
