Siberian Mathematical Journal

, Volume 44, Issue 5, pp 793–796 | Cite as

Some Conditions for a C0-Semigroup to Be Asymptotically Finite-Dimensional

  • E. Yu. Emel'yanov


We study the class of bounded C0-semigroups T=(T t )t≥0 on a Banach space X satisfying the asymptotic finite dimensionality condition: codim X0(T)<∞, where X0(T):={xX:limt→∞T t x❘=0}. We prove a theorem which provides some necessary and sufficient conditions for asymptotic finite dimensionality.

C0-semigroup invariant subspace of a semigroup almost periodic semigroup 


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  1. 1.
    Emel'yanov E. Yu. and Wolff M. P. H., “Quasi constricted linear operators on Banach spaces,” Studia Math., 144, No. 2, 169–179 (2001).Google Scholar
  2. 2.
    Emel'yanov E. Yu. and Wolff M. P. H., “Quasi constricted linear representations of abelian semigroups on Banach spaces,” Math. Nachr., 233-234, 103–110 (2002).Google Scholar
  3. 3.
    Vu Kuok Fong, “Asymptotic almost-periodicity and compactifying representations of semigroups,” Ukrainian Math. J., 38, 688–692 (1986).Google Scholar
  4. 4.
    Sine R., “Constricted systems,” Rocky Mountain J. Math., 21, 1373–1383 (1991).Google Scholar
  5. 5.
    Lyubich Yu. I., Introduction to the Theory of Banach Group Representations [in Russian], Vishcha Shkola (Izdat. pri Khar'kov. Gos. Univ.), Khar'kov (1985).Google Scholar
  6. 6.
    Kre?n M. G., Krasnose'ski? M. A., and Mil'man D. P., “On defect numbers of linear operators in Banach space and some geometric questions,” Sb. Trudov Inst. Mat. Akad. Nauk Ukrain. SSR, 11, 97–112 (1948).Google Scholar
  7. 7.
    Gokhberg I. Ts. and Kre?n M. G., “Main aspects of defect numbers, root numbers, and indices of linear operators,” Uspekhi Mat. Nauk, 3, No. 1, 43–118 (1957).Google Scholar
  8. 8.
    Albeverio S., Fenstad J. F., Höegh-Krohn R. J., and Lindström T. L., Nonstandard Methods in Stochastic Analysis and Mathematical Physics [Russian translation], Mir, Moscow (1990).Google Scholar
  9. 9.
    Henson C.W. and Moore L. C. Jr., “Nonstandard analysis and the theory of Banach spaces,” in: Nonstandard Analysis-Recent Developments, Springer-Verlag, Berlin etc., 1983, pp. 27–112 (Lecture Notes in Math.; 983).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • E. Yu. Emel'yanov
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirsk

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