Operators with Simple Orbital Behavior

Part of the Fields Institute Communications book series (FIC, volume 81)


In this paper we consider two similarity-invariant classes of operators on a complex Hilbert space. A complete description, in terms of properties of various parts of the spectrum, is obtained for the operators in the closure and for the operators in the interior of each of these classes.


Orbital behavior Fredholm Closure Interior 

Msc codes

Primary 47A58; Secondary 47A56, 47L30 


  1. 1.
    Apostol, C. Matrix models for operators, Duke Math. J. 42 (1975), 779–785.MathSciNetMATHGoogle Scholar
  2. 2.
    Apostol, C. The correction by compact perturbations of the singular behavior of operators, Rev. Roum. Math. Pures et Appl. 21 (1976), 155–175.MathSciNetMATHGoogle Scholar
  3. 3.
    Apostol, C.; Fialkow, L.A.; Herrero, D.A.; Voiculescu, D. Approximation of Hilbert space operators. II., Pitman Publ. Inc., Boston-London-Melbourne, 1984.Google Scholar
  4. 4.
    Apostol, C.; Morrel, B.B. On uniform approximation of operators by simple models, Indiana Univ. Math. J. 26(1977), 427–442.MathSciNetMATHGoogle Scholar
  5. 5.
    Conway, J. B. A course in functional analysis, Springer-Verlag, New York, second ed., 1990.MATHGoogle Scholar
  6. 6.
    Halmos, P. R. Ten problems in Hilbert space, Bull. Amer. Math. Soc. 5(1970), 887–933.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Herrero, D. A. Approximation of Hilbert space operators. I., Pitman Publ. Inc., Boston-London-Melbourne, 1982.Google Scholar
  8. 8.
    Muller, V. Local spectral radius formula for operators on Banach spaces, Czech. Math. J. 38(1988), 726–729.MathSciNetMATHGoogle Scholar
  9. 9.
    Prǎjiturǎ, G.T. The geometry of an orbit Operator Theory Live, 145–154, Theta, Bucharest, 2010.Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State University of New YorkBrockportUSA

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