Skip to main content
SpringerLink
Log in

A note on vanishing of the functor ext1 for Köthe spaces

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

In this note we study the relationship between the vanishing of Ext1(λ(A), λ(A)) and the existence of a regular basis in the Köthe space λ(A). We construct an example of a nuclear Köthe space λ(A) with no regular basis and such that Ext1(λ(A), λ(A))=0. Then we show that for some classes of Köthe spaces λ(A), the vanishing of Ext1(λ(A), λ(A)) yields a regular basis for λ(A).

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. Bessaga, C.: Some remarks on Dragilev's theorem. Studia Math.31, 307–318 (1968)

    MathSciNet  MATH  Google Scholar 

  2. Crone, L., Dubinsky, E., Robinson, W.B.: Regular bases in products of power series spaces. J. Funct. Anal.24, 211–222 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dragilev, M.M.: On regular bases in nuclear spaces. Math. Sb.68, 153–173 (1965) (Amer. Math. Soc. Transl.93, 61–82 (1970))

    MathSciNet  MATH  Google Scholar 

  4. Dubinsky, E.: The structure of nuclear Fréchet spaces. Lecture Notes in Mathematics 720 (1979)

  5. Hebbecker, J.: Auswertung der Splittingbedingungen (S *1 ) und (S *2 ) für Potenzreihenräume undL f -Räume. Diplomarbeit, Wuppertal, 1984

  6. Kocatepe, M., Nurlu, Z.: Some special Köthe spaces. Advances in the theory of Fréchet spaces (ed: T. Terzioğlu) 269–296, NATO ASI Series, Series C 287 (1989)

  7. Krone, J.: Zur topologischen Charakterisierung von Unter- und Quotientenräumen spezieller nuklearer Kötheräume mit der Splittingmethode. Diplomarbeit, Wuppertal, 1984

  8. Krone, J., Vogt, D.: The splitting relation for Köthe spaces. Math. Z.180, 387–400 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  9. Robinson, W.B.: Relationships between λ-nuclearity and pseudo-μ-nuclearity. Trans. Amer. Math. Soc.201, 291–303 (1975)

    MathSciNet  MATH  Google Scholar 

  10. Vogt, D.: Charakterisierung der Unterräume vons. Math. Z.155, 109–117 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  11. Vogt, D.: On the functors Ext1(E, F) for Fréchet spaces. Studia Math.85, 163–197 (1987)

    MathSciNet  Google Scholar 

  12. Wagner, M.J.: Quotientenräume von stabilen Potenzreihenräumen endlichen Typs. manus. math.31, 97–109 (1980)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics Faculty of Engineering and Science, Bilkent University, 06533, Bilkent, Ankara, Turkey

    Mefharet Kocatepe

Authors
  1. Mefharet Kocatepe
    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

Kocatepe, M. A note on vanishing of the functor ext1 for Köthe spaces. Manuscripta Math 71, 113–119 (1991). https://doi.org/10.1007/BF02568397

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02568397

Keywords

Search

Navigation