Skip to main content

A simple-minded proof of the Pisier-grothendieck inequality

Part of the Lecture Notes in Mathematics book series (LNM,volume 995)

Keywords

  • Banach Space
  • Bilinear Form
  • Main Lemma
  • Compact Hausdorff Space
  • Commutative Case

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. C. Blei, A uniformity property for λ(2) sets and Grothendieck’s inequality. Symposia Math. Vol. XXII (1977) 321–336.

    MathSciNet  Google Scholar 

  2. J. F. Fournier, On a theorem of Paley and the Littlewood conjecture. Arkiv för Matematik 17 (1979) 199–216.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. A. Grothendieck, Résumé de la théorie métrique des produits tensoriels topologiques. Bol. Soc. Mat. Brasil, Sao Paulo, 8 (1956), 1–79.

    MATH  Google Scholar 

  4. J. L. Krivine, Théorèmes de factorisations dans les espaces réticulés. Sém. Maurey-Schwarz 73–74, exp. XXII–XXIII.

    Google Scholar 

  5. J. Lindenstrass and A. Pelczynski, Absolutely p-summing operators in L p-spaces and their applications. Studia Math. 29 (1968) 275–326.

    MathSciNet  Google Scholar 

  6. J. Lindenstrass and L. Tzafriri, Classical Banach spaces. Springer, Berlin-Heidelberg-New York 1977.

    CrossRef  Google Scholar 

  7. M. A. Naimark, Normed rings. P. Noordhoff N.V. Groningen 1964.

    Google Scholar 

  8. B. Maurey, Une nouvelle démonstration d’un theorème de Grothendieck. Sém. Maurey-Schwarz 72–73, exp. XXII.

    Google Scholar 

  9. A. Pelczynski, Banach spaces of analytic functions and absolutely summing operators. C.B.M.S. Regional Conference Series in Mathematics, 30, 1977.

    Google Scholar 

  10. G. Pisier, Grothendieck’s theorem for non-cummutative C*-algebras with an appendix on Grothendieck’s constants. J. Funct. Anal. 29 (1978) 397–415.

    CrossRef  MathSciNet  MATH  Google Scholar 

References for the Appendix

  1. Bohnenblust, H. F., and Karlin, S., Geometrical properties of the unit sphere of Banach algebras. Ann. of Math. 62 (1955) 217–229.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Haagerup, Uffe, The Grothendieck inequality for bilinear forms on C*-algebras. Preprint, Odense University.

    Google Scholar 

  3. Kaijser, S., Representations of tensor algebras as quotients of group algebras. Arkiv f. Mat. 10 (1972) 107–141.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Tomczak-Jaegermann., On the moduli of smoothness and convexity and the Rademacher averages of the trace classes Sp (1≤p<∞). Studia Math. 50 (1974) 163–182.

    MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Kaijser, S. (1983). A simple-minded proof of the Pisier-grothendieck inequality. In: Blei, R.C., Sidney, S.J. (eds) Banach Spaces, Harmonic Analysis, and Probability Theory. Lecture Notes in Mathematics, vol 995. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061887

Download citation

  • DOI: https://doi.org/10.1007/BFb0061887

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12314-9

  • Online ISBN: 978-3-540-40036-3

  • eBook Packages: Springer Book Archive