Skip to main content
SpringerLink
Log in

Semi-Fredholm operators and sequence conditions

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

A typical result of this paper is the following: A closed linear operator T between Banach spaces X and Y is lower semi-Fredholm iff it is a rk-(=relatively compact)surjection, i.e. for every bounded sequence (yn) in Y there is a bounded sequence (xn) in D(T) such that (yn−Txn) is relatively compact in Y. The concept of co-(rk- and wk-)injections and surjections are introduced to characterize semi-Fredholm properties (in the usual or generalized sense). This is done also by new operator moduli.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. BERBERIAN, S.K.: Approximate proper values. Proc. Amer. Math. Soc.13, 111–114 (1962)

    Google Scholar 

  2. BUONI, J.J., HARTE, R.E. and WICKSTEAD, A.W.: Upper and lower Fredholm spectra. Proc. Amer. Math. Soc.66, 309–314 (1977)

    Google Scholar 

  3. BUONI, J.J., KLEIN,A.: On the generalized Calkin algebra. Pacific J. Math.80, 9–12 (1979)

    Google Scholar 

  4. CHADWICK, J.J.M., WICKSTEAD, A.W.: A quotient of ultrapowers of Banach spaces and semi-Fredholm operators. Bull. London Math. Soc.9, 321–325 (1977)

    Google Scholar 

  5. FÖRSTER, K.-H., LIEBETRAU, E.-O.: On semi-Fredholm operators and the conjugate of a product of operators. Studia Math.49, 301–306 (1977)

    Google Scholar 

  6. GINDLER, H.A., TAYLOR, A.E.: The minimal modulus of a linear operator and its use in spectral theory. Studia Math.22, 15–41 (1962)

    Google Scholar 

  7. GOLDBERG, S.: Unbounded linear operators. New York: McGraw-Hill 1966

    Google Scholar 

  8. HARTE, R.E.: Berberian-Quigley and the ghost of a spectral mapping theorem. Proc. R.I.A:78, 63–68 (1978)

    Google Scholar 

  9. HARTE, R.E., WICKSTEAD, A.W.: Upper and lower Fredholm spectra II. Math. Z.154, 253–256 (1977)

    Google Scholar 

  10. KAUFMAN, R.: Operators with closed range. Proc. Amer. Math. Soc.17, 767–768 (1966)

    Google Scholar 

  11. PIETSCH, A.: Operator ideals. Berlin: VEB Deutscher Verlag der Wissenschaften 1978

    Google Scholar 

  12. PRÖSSDORF, S.: Einige Klassen singulärer Gleichungen. Basel: Birkhäuser Verlag 1974

    Google Scholar 

  13. SADOVSKII, B.N.: Limit-compact and condensing operators. Russ. Math. Surveys27, 85–155 (1972)

    Google Scholar 

  14. YANG, K.-W.: The generalized Fredholm operators. Trans. Amer. Math. Soc.216, 313–326 (1976)

    Google Scholar 

  15. YANG, K.-W.: Operators invertible modulo the weakly compact operators. Pacific J. Math.71, 559–564 (1977)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich 3 (Mathematik), Technische Universität Berlin, Strasse d. 17. Juni 135, 1000, Berlin 12, Federal Republic of Germany

    K. -H. Förster

  2. Fachbereich 6 (Mathematik/Informatik), Universität Oldenburg, Ammerländer Heerstr. 67-99, 2900, Oldenburg, Federal Republic of Germany

    E. -O. Liebetrau

Authors
  1. K. -H. Förster
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. -O. Liebetrau
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Förster, K.H., Liebetrau, E.O. Semi-Fredholm operators and sequence conditions. Manuscripta Math 44, 35–44 (1983). https://doi.org/10.1007/BF01166071

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01166071

Keywords

Search

Navigation