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Every $ n\times n$ matrix $ Z$ with real spectrum satisfies $ \Vert Z-Z\sp{\ast}\Vert \leq \Vert Z+Z\sp{\ast} \Vert(\log\sb{2}n+0.038)$


Author: W. Kahan
Journal: Proc. Amer. Math. Soc. 39 (1973), 235-241
MSC: Primary 15A60
DOI: https://doi.org/10.1090/S0002-9939-1973-0313278-3
MathSciNet review: 0313278
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Abstract: The title's inequality is proved for the operator bound-norm in a unitary space. An example is exhibited to show that the inequality cannot be improved by more than about 8


References [Enhancements On Off] (What's this?)

  • [1971] Chandler Davis, The Toeplitz-Hausdorff theorem explained, Canad. Math. Bull. 14 (1971), 245-246. MR 0312288 (47:850)
  • [1958] Ulf Grenander and Gabor Szegö, Toeplitz forms and their applications, Univ. of California Press, Berkeley, Calif., 1958. MR 20 #1349. MR 0094840 (20:1349)
  • [1971] Alan McIntosh, Counterexample to a question on commutators, Proc. Amer. Math. Soc. 29 (1971), 337-340. MR 43 #2538. MR 0276798 (43:2538)
  • [1972] -, On the comparability of $ {A^{1/2}}$ and $ {({A^ \ast })^{1/2}}$, Proc. Amer. Math. Soc. 32 (1972), 430-434. MR 44 #7354. MR 0290169 (44:7354)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0313278-3
Keywords: Matrix with real spectrum, numerical range
Article copyright: © Copyright 1973 American Mathematical Society

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