Spectral, and Numerical Range, Approximants

  • Philip J. Maher


The theory of spectral approximants presents a precise geometric way of specifying approximants. The theory was initiated by Halmos [22] and later extended to the context of \(\mathcal{C}_{p}\) by Bouldin [11] and Bhatia [8]. More recently the related concept of numerical range approximant was introduced [25].


  1. 7.
    S.K. Berberian, The Weyl spectrum of an operator. Indiana Univ. Math. J. 20, 529–544 (1970)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 8.
    R. Bhatia, Some inequalities for norm ideals. Commun. Math. Phys. 111, 33–39 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 11.
    R. Bouldin, Best approximation of a normal operator in the Schatten p-norm. Proc. Am. Math. Soc. 80, 277–282 (1980)MathSciNetzbMATHGoogle Scholar
  4. 22.
    P.R. Halmos, Spectral approximants of normal operators. Proc. Edin. Math. Soc. 19, 51–58 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 23.
    P.R. Halmos, A Hilbert Space Problem Book, 2nd edn. (Springer, New York, 1974)CrossRefzbMATHGoogle Scholar
  6. 25.
    R. Khalil, P.J. Maher, Spectral approximation in L(H). Numer. Funct. Anal. Optim. 21(5/6), 693–713 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 34.
    P.J. Maher, Spectral approximants concerning balanced and convex sets. Ann. Univ. Sci. Budapest. 46, 177–181 (2003)zbMATHGoogle Scholar
  8. 41.
    D.D. Rogers, Approximation by unitary and essentially unitary operators. Acta Sci. Math. 39, 141–151 (1977)MathSciNetzbMATHGoogle Scholar
  9. 43.
    B. Simon, Trace Ideals and Their Applications (Cambridge University Press, Cambridge, 1979)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

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

Personalised recommendations