Skip to main content
SpringerLink
Log in

Fredholm operator families —II

  • Published:
Integral Equations and Operator Theory Aims and scope Submit manuscript

Abstract

This paper is a continuation of a former one which has appeared in this journal. After considering (continuous and smooth) bundles of subspaces of an arbitrary topological vector space (tvs) we show how they appear naturally as image or kernel of semi-Fredholm families. We also extend some well known results of holomorphic Fredholm families to the setting of arbitrary tvs.

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. Bart, H., Kaashoek, M. A. and Lay, D. C.: Relative Inverses of Meromorphic Operator Functions and Associated Holomorphic Projection Functions. Math. Ann. 218, 199–210 (1975).

    Google Scholar 

  2. Cuéllar, J., Dynin A. and Dynin S.: Fredholm Operator FamiliesI. Integral Equations and Operator Theory (1983).

  3. Gramsch, B.: Inversion von Fredholmfunktionen bei stetiger und holomorpher Abhängigkeit von Parametern. Math. Ann. 214, 95–147 (1975).

    Google Scholar 

  4. Gramsch, B. and Kaballo, W.: Spectral Theory for Fredholm Operators. In: Functional Analysis: Surveys and Recent Results II, 319–342. Ed.: K.D. Bierstedt, B. Fuchssteiner. North-Holland. Amsterdam (1980).

    Google Scholar 

  5. Hörmander, L.: On the Index of Pseudodifferential Operators. In: Elliptische Differentialgleichungen. Band II. 127–146. Akademie-Verlag. Berlin (1971).

    Google Scholar 

  6. Kaballo, W.: Projektoren und relative Inversion holomorpher Semi-Fredholmfunktionen. Math. Ann. 219, 85–96 (1976).

    Google Scholar 

  7. Mennicken, R. and Sagraloff, B.: Analitic Perturbation of Semi-Fredholm Operators. Math. Ann. 254, 177–188 (1980).

    Google Scholar 

  8. Markoe, A.: Analitic Families of Differential Complexes. J. Funct. Anal. 9, 181–188 (1972).

    Google Scholar 

  9. Segal, G.: Fredholm Complexes. Quart. J. Math. Oxford (2), 21, 385–402 (1970).

    Google Scholar 

  10. Shubin, M.A.: On Holomorphic Families of Subspaces of a Banach Space. Integral Equations and Operator Theory 2, 407–420 (1979). Translated from Mat. Issled 5, 153–165 (1970).

    Google Scholar 

  11. Zaidenberg, M.G., Krein, S.G., Kuchment, P.A., Pankov, A.A.: Banach Bundles and Linear Operators. Russian Math. Surveys 30:5, 115–175 (1975). Translated from Uspekhi mat. Nauk 30:5, 101–157 (1975).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Universität Mainz, D-6500, Mainz, Federal Republic of Germany

    Jorge Cuellar

  2. Department of Mathematics, The Ohio State University, 231 West 18th Avenue, 43210, Columbus, Ohio, USA

    Alexander Dynin & Svetlana Dynin

Authors
  1. Jorge Cuellar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander Dynin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Svetlana Dynin
    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

Cuellar, J., Dynin, A. & Dynin, S. Fredholm operator families —II . Integr equ oper theory 7, 36–44 (1984). https://doi.org/10.1007/BF01204912

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01204912

Keywords

Search

Navigation