Skip to main content

Multiple Tensor Norms of Michor’s Type and Associated Operator Ideals

In Honour of Manuel López-Pellicer

  • Conference paper
  • First Online:
Descriptive Topology and Functional Analysis II (TFA 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 286))

Included in the following conference series:

Abstract

We study the \((n+1)\)-tensor norms of Michor type and characterize the n-linear mappings of the components of its associated operator ideals.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

References

  1. Aliprantis, C.D., Burkinshaw, O.: Positive Operators. Academic Press, New York (1985)

    MATH  Google Scholar 

  2. Day, M.M.: Normed Linear Spaces. Springer, Berlin (1973)

    Book  Google Scholar 

  3. Defant, A., Floret, K.: Tensor Norms and Operator Ideals. North Holland, Amsterdam (1993)

    MATH  Google Scholar 

  4. Diestel, J., Jarchow, H., Tonge, A.: Absolutely Summing Operators. Camdridge University Press, Cambridge (1995)

    Book  Google Scholar 

  5. Dukaric, D.D: The Hilbertian tensor norm and entangles two-prover games. New J Phys. 13, 1–33 (2011)

    Article  MathSciNet  Google Scholar 

  6. Floret, K., Hunfeld, S.: Ultrastability of ideals of homogeneous polynomials and multilinear mappings on Banach spaces. Proc. Am. Math. Soc. 130(5), 1425–1435 (2002)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  8. Haydon, R., Levy, M., Raynaud, Y.: Randomly Normed Spaces. Herman, París (1991)

    MATH  Google Scholar 

  9. Heinrich, S.: Ultraproducts in Banach space theory. J. Reine Angew. Math. 313, 72–104 (1980)

    MathSciNet  MATH  Google Scholar 

  10. Henson, C.W., Moore jr., L.C.: Nonstandard analysis and theory of Banach spaces. In: Hurd, A.E. (eds.) Non Standard Analysis-recent Developments, pp. 27–112. Springer, Berlin (1983)

    Google Scholar 

  11. Hewitt, E., Stromberg, K.: Real and Abstract Analysis. Springer, Berlin (1969)

    MATH  Google Scholar 

  12. Kürsten, K.D.: Local duality of ultraproducts of Banach lattices. In: Pietsch, A., Popa, N., Singer, I. (eds.) Banach Space Theory and its Applications, pp. 137–142. Springer, Berlin (1983)

    Chapter  Google Scholar 

  13. Lapresté, J. T.: Opérateurs sommants et factorisations à travers les espaces \(L^p.\) Studia Math. 57, 47–83 (1976)

    Article  MathSciNet  Google Scholar 

  14. Lewis, D.R.: Duals of tensor products. In: Dold, A., Eckmann, B. (eds.) Banach spaces of Analytic Functions, pp. 57–66. Springer, Berlin (1977)

    Chapter  Google Scholar 

  15. López Molina, J.A.: \((n+1)\)-tensor norms of Lapresté’s type. Glasgow Math. J. 54, 665–692 (2012)

    Article  MathSciNet  Google Scholar 

  16. López Molina, J.A.: The minimal and maximal operator ideals associated to \((n+1)\)-tensor norms of Michor’s type. Positivity 22, 1109–1142 (2018)

    Article  MathSciNet  Google Scholar 

  17. Lotz, H.P.: Grothendieck Ideals of Operators in Banach Spaces. Unpublished Lecture Notes University of Illinois, Urbana (1973)

    Google Scholar 

  18. Maharam, D.: The representation of abstract measure functions. Trans. Am. Math. Soc. 65, 279–330 (1949)

    Article  MathSciNet  Google Scholar 

  19. Maharam, D.: Decompositions of measure algebras and spaces. Trans. Am. Math. Soc. 69, 142–160 (1950)

    Article  MathSciNet  Google Scholar 

  20. Mazur, S., Ulam, S.: Sur les transformations isométriques d’espaces vectoriels. C. R. Acad. Sci. Paris 194, 946–948 (1932)

    MATH  Google Scholar 

  21. Michor, P.W.: Functors and Categories of Banach Spaces. Springer, Berlin (1978)

    Book  Google Scholar 

  22. Pietsch, A.: Operator Ideals. North Holland, Amsterdam (1980)

    MATH  Google Scholar 

  23. Pietsch, A.: Ideals of multilinear functionals (designs of a theory). In: Proceeding of the Second International Conference on Operator Algebras. Ideals and Their Applications in Theoretical Physics, Leipzig 1983, pp. 185–199. Teubner-Texte, Leipzig (1983)

    Google Scholar 

  24. Raynaud, Y.: Ultrapowers of Calderón-Lozanowkii interpolation spaces. Indag. Math., N. S. 9 (1), 65–105 (1998)

    Article  MathSciNet  Google Scholar 

  25. Schatten, R.: A theory of cross-spaces. Ann. Math. Stud. 26 (1950)

    Google Scholar 

  26. Schreiber, M.: Quelques remarques sur les charactérisations des spaces \(L^p, 0\le p<1.\) Ann. Inst. Henri Poincaré VIII 1, 83–92 (1972)

    Google Scholar 

  27. Sickel, W., Ulrich, T.: Tensor products of Sobolev-Besov spaces and applications to approximation from the hyperbolic cross. J. Approx. Th. 161, 748–786 (2009)

    Article  MathSciNet  Google Scholar 

  28. Wnuk, W., Wiatrowski, B.: When are ultrapowers lattices discrete or continuous? In: Proceedings Positiviy IV-Theory and Applications, pp. 173–182. Dresden (2006)

    Google Scholar 

  29. Zaanen, A.C.: Integration. North-Holland, Amsterdam (1967)

    MATH  Google Scholar 

Download references

Acknowledgements

I express my gratitude to the Organization of the Meeting in honour to Prof. López Pellicer for its invitation to present a talk.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Juan Antonio López Molina .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

López Molina, J.A. (2019). Multiple Tensor Norms of Michor’s Type and Associated Operator Ideals. In: Ferrando, J. (eds) Descriptive Topology and Functional Analysis II. TFA 2018. Springer Proceedings in Mathematics & Statistics, vol 286. Springer, Cham. https://doi.org/10.1007/978-3-030-17376-0_11

Download citation

Publish with us

Policies and ethics