Unitary, Isometric and Partially Isometric Approximation of Positive Operators

  • Philip J. Maher


This chapter is about approximation of positive operators by operators that in some sense preserve size: by—in ascending order of generality—unitaries, isometries and partial isometries.


  1. 1.
    J.G. Aiken, J.A. Erdos, J.A. Goldstein, Unitary approximation of positive operators. Ill. J. Math. 24, 61–72 (1980)MathSciNetzbMATHGoogle Scholar
  2. 2.
    J.G. Aikten, J.A. Erdos, J.A. Goldstein, On Lowdin orthogonalization. Int. J. Quantum Chem. 18, 1101–1108 (1980)CrossRefGoogle Scholar
  3. 18.
    J.A. Goldstein, M. Levy, Linear algebra and quantum chemistry. Am. Math. Mon. 98, 710–718 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 23.
    P.R. Halmos, A Hilbert Space Problem Book, 2nd edn. (Springer, New York, 1974)CrossRefzbMATHGoogle Scholar
  5. 28.
    P.J. Maher, Partially isometric approximation of positive operators. Ill. J. Math. 33, 227–243 (1989)MathSciNetzbMATHGoogle Scholar
  6. 34.
    P.J. Maher, Spectral approximants concerning balanced and convex sets. Ann. Univ. Sci. Budapest. 46, 177–181 (2003)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Philip J. Maher
    • 1
  1. 1.LondonUK

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