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Proceedings of the American Mathematical Society

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

 
 

 

Nearest normal approximation for certain operators


Author: John Phillips
Journal: Proc. Amer. Math. Soc. 67 (1977), 236-240
MSC: Primary 47A55; Secondary 47B20
DOI: https://doi.org/10.1090/S0002-9939-1977-0458212-4
MathSciNet review: 0458212
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Abstract: In this paper we show that binormal operators have nearest normal approximants. In fact, we exhibit nearest normals to such operators and, as a corollary, show that the hermitian part of a binormal operator with real spectrum is a nearest normal. We obtain further corollaries on nearest normal approximation to operators which are square roots of normal operators and then apply these results to perturbations of operator algebras.


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  • [1] E. Christensen, Perturbations of type I von Neumann algebras, J. London Math. Soc. 9 (1975), 395-405. MR 0358373 (50:10839)
  • [2] -, Perturbations of operator algebras, Univ. of Oslo preprint series, no. 14, 1974.
  • [3] K. Fan and A. J. Hoffman, Some metric inequalities in the space of matrices, Proc. Amer. Math. Soc. 6 (1955), 111-116. MR 0067841 (16:784j)
  • [4] P. R. Halmos, Positive approximants of operators, Indiana Univ. Math. J. 21 (1972), 951-960. MR 0291829 (45:919)
  • [5] -, Spectral approximants of normal operators, Proc. Edinburgh Math. Soc. 19 (1974), 51-58. MR 0344935 (49:9674)
  • [6] R. V. Kadison and D. Kastler, Perturbations of von Neumann algebras. I: Stability of type, Amer. J. Math. 94 (1972), 38-54. MR 0296713 (45:5772)
  • [7] H. Radjavi and P. Rosenthal, On roots of normal operators, J. Math. Anal. Appl. 34 (1971), 653-664. MR 0278097 (43:3829)
  • [8] -, Invariant subspaces, Springer-Verlag, New York, 1973. MR 0367682 (51:3924)
  • [9] D. J. van Riemsdijk, Some metric inequalities in the space of bounded linear operators on a separable Hilbert space, Nieuw Arch. Wisk. (3) 20 (1972), 216-230. MR 0328632 (48:6974)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0458212-4
Keywords: Normal operator, binormal operator, normal approximation, perturbations of operator algebras
Article copyright: © Copyright 1977 American Mathematical Society

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