Skip to main content
SpringerLink
Log in

Some problems on bases in Banach and frechet spaces

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

This paper is a revised version of the author’s report during the Symposium “On Series and Geometry in Linear Spaces” held at The Hebrew University of Jerusalem, March 16–24, 1964. Some problems of the existence (for a given Frechet space) of closed linear subspaces and quotient spaces with bases are discussed.

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. K. I. Babienko,On conjugate functions, Dokl. Akad. Nauk. SSSR62 (1948), 157–160 (in Russian).

    Google Scholar 

  2. S. Banach,Théorie des opérations linéaires, Warszawa, 1932.

  3. N. K. Bari,Biorthogonal systems and bases in Hilbert space, Učen. Zap. Moskov. Gos, Univ.,148 (1951), 69–107 (in Russian).

    MathSciNet  Google Scholar 

  4. C. Bessaga and A. Pełczyński,On bases and unconditional convergence of series in Banach spaces, Studia Math.17 (1958), 151–164.

    MATH  MathSciNet  Google Scholar 

  5. C. Bessaga and A. Pełczyński,Properties of bases in B 0 spaces, Prace Mat.3 (1959), 123–142 (in Polish).

    MATH  MathSciNet  Google Scholar 

  6. C. Bessaga and A. Pełczyński,A generalization of results of R. C. James concerning absolute bases in Banach spaces, Studia Math.17 (1958), 165–174.

    MATH  MathSciNet  Google Scholar 

  7. C. Bessaga and A. Pełczyński,Some remarks on homeomorphism of Banach spaces, Bull. Acad. Polon. Sci., Sér. sci. math., astr. et phys.8 (1960), 757–761.

    Google Scholar 

  8. C. Bessaga, A. Pełczyński and S. Rolewicz,On diametral approximative dimension and linear homogenity of F-spaces, Bull. Acad. Polon. Sci., Sér. sci. math., astr. et phys.9 (1961), 677–683.

    MATH  Google Scholar 

  9. M. M. Day,On basis problem in Banach spaces, Proc. Amer. Math. Soc.13 (1962). 655–658.

    Article  MATH  MathSciNet  Google Scholar 

  10. A. Dvoretzky,Some results on convex bodies and Banach spaces, Proc. of the International Symposium on Linear Spaces, Jerusalem 1961, 123–160.

  11. A. S. Dynin and B. S. Mitiagin,Criterion for nuclearity in terms of approximative dimension, Bull. Acad. Polon. Sci., Sér. sci. math., astr. et phys.8 (1960), 535–540.

    MATH  MathSciNet  Google Scholar 

  12. M. Eidelheit,Zur Theorie der Systeme linearer Gleichungen, Studia Math.6 (1936), 139–148.

    MATH  Google Scholar 

  13. B. R. Gelbaum,Banach spaces and bases, An. Acad. Brasil. Ci.30 (1958), 29–36.

    MathSciNet  Google Scholar 

  14. I. M. Gelfand,A remark to the paper of N. K. Bari “Biorthogonal systems and bases in Hilbert space,” Učen. en. Zap. Moskov. Gos. Univ.148 (1951), 224–225. (in Russian).

    Google Scholar 

  15. V. I. Gurarij,On slopes of subspaces and conditional bases in Banach spaces, Dokl. Akad. Nauk. SSSR145 (1962), 504–506. (in Russian).

    MathSciNet  Google Scholar 

  16. R. C. James,Bases and reflexivity of Banach spaces, Ann. of Math.52 (1950), 518–527.

    Article  MathSciNet  Google Scholar 

  17. M. I. Kadec and A. Pełczyński,Basic sequences and norming sets in Banach and Fréchet spaces, Studia Math. (to appear) (in russian).

  18. B. S. Mitiagin,Approximative dimension and bases in nuclear spaces, Uspehi Mat. Nauk.14 (100) (1961), 63–132.

    Google Scholar 

  19. A. Pełczyński,Projections in certain Banach spaces, Studia Math.19 (1960), 209–228.

    MathSciNet  Google Scholar 

  20. A. Pełczyński,A note on the paper of I. Singer “Basic sequences and reflexivity of Banach spaces”, Studia Math.21 (1962), 371–374.

    MathSciNet  Google Scholar 

  21. A. Pełczyński and I. Singer,On non equivalent bases and conditional bases in Banach spaces, Studia Math.25 (1965), 5–25.

    MathSciNet  Google Scholar 

  22. R. C. James,Weakly compact sets, Trans. Amer. Math. Soc.113 (1964), 129–140

    Article  MATH  MathSciNet  Google Scholar 

  23. V. Klee Jr.,On the Borelian projective types of linear subspaces, Math. Scand.6 (1958), 189–199.

    MATH  MathSciNet  Google Scholar 

  24. J. Lindenstrauss,On a subspace of the space l, Bull. Acad. Polon. Sci. des Sci. Math. astr. et phys.12 (1964), 539–542.

    MATH  MathSciNet  Google Scholar 

  25. A. Pełczyński,A proof of Eberlein-Smulian theorem by an application of basic sequences. Bull. Acad. Polon. Sci., Sér. des Sci. Math. astr. et phys.12 (1964), 543–548.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Warsaw, Poland

    A. Pełczyński

Authors
  1. A. Pełczyński
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Lecture delivered at a symposium on Series and Geometry in Linear Spaces, held at the Hebrew University of Jerusalem from March 16 till March 24, 1964.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pełczyński, A. Some problems on bases in Banach and frechet spaces. Israel J. Math. 2, 132–138 (1964). https://doi.org/10.1007/BF02759953

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02759953

Keywords

Search

Navigation