Skip to main content

Grothendieck’s inequality and minimal orthogonally scattered dilations

Part of the Lecture Notes in Mathematics book series (LNM,volume 1080)

Keywords

  • Hilbert Space
  • Radon Measure
  • Vector Measure
  • Reproduce Kernel Hilbert Space
  • Compact Hausdorff Space

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   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
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. Abreu, J.L.: A note on harmonizable and stationary sequences. Bol. Soc. Mat. Mexicana15, 48–51, (1970).

    MathSciNet  MATH  Google Scholar 

  2. Aronszajn, N.: Theory of reproducing kernels. Trans. Amer. Math. Soc.68, 337–404, (1950).

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Chatterji, S.D.: Orthogonally scattered dilation of Hilbert space valued set functions. In Measure Theory. Proc. Conf. Oberwolfach 1981. (D. Kölzow and D. Maharam-Stone, Eds.), pp. 269–281. Lecture Notes in Mathematics 945, Springer-Verlag, Berlin/Heidelberg/New York, (1982).

    Google Scholar 

  4. Goldstein, S. and Jajte, R.: Second-order fields over W*-algebras. Bull. Acad. Polon. Sci. Sér. Sci. Math.30, 255–260, (1982).

    MathSciNet  MATH  Google Scholar 

  5. Grothendieck, A.: Résumé de la théorie métrique des produits tensoriels topologiques. Bol. Soc. Mat. São Paulo8, 1–79, (1956).

    MATH  Google Scholar 

  6. Kluvánek, I.: Characterization of Fourier-Stieltjes transforms of vector and operator valued measures. Czechoslovak Math. J.17 (92), 261–277, (1967).

    MathSciNet  MATH  Google Scholar 

  7. Krivine, J.L.: Sur la complexification des opérateurs de L dans L1. C.R. Acad. Sci. Paris Ser. A284, 377–379, (1977).

    MathSciNet  MATH  Google Scholar 

  8. Krivine, J.L.: Sur la constante de Grothendieck. C.R. Acad. Sci. Paris Ser. A284, 445–446, (1977).

    MathSciNet  MATH  Google Scholar 

  9. Krivine, J.L.: Constantes de Grothendieck et fonctions de type positif sur les sphères. Adv. in Math.31, 16–30, (1979).

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Lindenstrauss, J. and Pezczynski, A.: Absolutely summing operators in lp spaces and their applications. Studia Math.29, 275–326, (1968).

    MathSciNet  Google Scholar 

  11. Lindenstrauss, J. and Tzafriri, L.: Classical Banach Spaces I. Ergebnisse der Mathematik und ihrer Grenzgebiete 92. Springer-Verlag. Berlin/Heidelberg/New York, (1977).

    CrossRef  MATH  Google Scholar 

  12. Miamee, A.G. and Salehi, H.: Harmonizability, V-boundness and stationary dilation of stochastic processes. Indiana Univ. Math. J.27, 37–50, (1978).

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Niemi, H.: On orthogonally scattered dilations of bounded vector measures. Ann. Acad. Sci. Fenn. Ser. A I Math.3, 43–52, (1977).

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Niemi, H.: On stationary dilations and the linear prediction of certain stochastic processes. Soc. Sci. Fenn. Comment. Phys.-Math.45, 111–130, (1975).

    MathSciNet  MATH  Google Scholar 

  15. Niemi, H.: On the construction of the Wold decomposition for nonstationary stochastic processes. Probab. Math. Statis.1, 73–82, (1980).

    MathSciNet  MATH  Google Scholar 

  16. Niemi, H.: Orthogonally scattered dilation of finitely additive vector measures in a Hilbert space. In Prediction Theory and Harmonic Analysis. (V. Mandrekar and H. Salehi, Eds.) pp. 233–251, North Holland Publishing Co., Amsterdam/New York/Oxford, (1983).

    Google Scholar 

  17. Persson, A. and Pietsch, A.: p-nukleare und p-integrale Abbildungen in Banachräumen. Studia Math.33, 19–62, (1969).

    MathSciNet  MATH  Google Scholar 

  18. Pietsch, A.: p-majorisierbare vektorwertige Masse. Wiss. Z. Friedrich-Schiller-Univ. Jena Math. Natur. Reihe18, 243–247, (1969).

    MathSciNet  MATH  Google Scholar 

  19. Pietsch, A.: Operator Ideals. Mathematische Monographien 16. VEB Deutscher Verlag der Wissenschaften, Berlin (1978).

    MATH  Google Scholar 

  20. Pisier, G.: Grothendieck’s theorem for noncommutative C*-algebras with appendix on Grothendieck’s constants. J. Funct. Anal.29, 397–415, (1978).

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. Rao, M.M.: Harmonizable processes: Structure theory. Enseign. Math. (2) 28, 295–352, (1982).

    MathSciNet  MATH  Google Scholar 

  22. Rietz, R.E.: A proof of the Grothendieck inequality. Israel J. Math.19, 271–276, (1974).

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. Rogge, R.: Masse mit Werten in einem Hilbertraum. Wiss. Z. Friedrich-Schiller-Univ. Jena Math. Natur. Reihe18, 253–257, (1969).

    MathSciNet  MATH  Google Scholar 

  24. Rosenberg, M.: Quasi-isometric dilations of operator-valued measures and Grothendieck’s inequality. Pacific J. Math.103, 135–161, (1982).

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. Truong-Van, B.: Une généralisation du théorème de Kolmogorov-Aronszajn, processus V-bornés q-dimensionnels, domaine spectral, dilation stationnaires. Ann. Inst. H. Poincare Sect. B. (N.S.)17, 31–49, (1981).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Niemi, H. (1984). Grothendieck’s inequality and minimal orthogonally scattered dilations. In: Szynal, D., Weron, A. (eds) Probability Theory on Vector Spaces III. Lecture Notes in Mathematics, vol 1080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099795

Download citation

  • DOI: https://doi.org/10.1007/BFb0099795

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13388-9

  • Online ISBN: 978-3-540-38939-2

  • eBook Packages: Springer Book Archive