, Volume 12, Issue 2, pp 209–219 | Cite as

Invariant Subspaces of Collectively Compact Sets of Linear Operators



In this paper, we first give some invariant subspace results for collectively compact sets of operators in connection with the joint spectral radius of these sets. We then prove that any collectively compact set M in algΓ satisfies Berger-Wang formula, where Γ is a complete chain of subspaces of X.

Mathematics Subject Classification (2000)



Invariant subspace collectively compact set joint spectral radius 


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  1. 1.
    Y.A. Abramovich, C.D. Aliprantis, An invitation to operator theory. Graduate Stud Math., 50, Amer. Math. Soc. (2002).Google Scholar
  2. 2.
    P.M. Anselone, Collectively Compact Operator Approximation Theory and Applications to Integral Equations , Prentice-Hall Inc. (1971).Google Scholar
  3. 3.
    M.A. Berger, Y. Wang, Bounded semigroups of matrices, Linear Algebra Appl. 166 (1992), 21–27.Google Scholar
  4. 4.
    H. Radjavi, P. Rosenthal, Simultaneous Triangularization, Springer (2000).Google Scholar
  5. 5.
    P. Rosenthal, A. Soltysiak, Formulas for the joint spectral radius of non-commuting Banach algebra elements, Proc. Am. Math. Soc. 123 (9) (1995), 2705–2708.Google Scholar
  6. 6.
    G.C. Rota, W.G. Strang, A note on the joint spectral radius, Indag. Math. 22 (1960), 379–381.Google Scholar
  7. 7.
    V.S. Shulman, Yu.V. Turovskii, Joint spectral radius, operator semigroups and a problem of W.Wojtynski . J. Funct. Anal. 177 (2000), 383–441.Google Scholar
  8. 8.
    Yu.V. Turovskii, Volterra semigroups have invariant subspaces, J. Funct. Anal. 162 (1999), 313–322.Google Scholar

Copyright information

© Springer Science + Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of MathematicsMiddle East Technical UniversityAnkaraRepublic of Turkey
  2. 2.Department of MathematicsIstanbul Technical UniversityMaslak-IstanbulRepublic of Turkey

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