Duke Mathematical Journal

Schatten-von Neumann classes of multilinear forms

Fernando Cobos, Thomas Kühn, and Jaak Peetre

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Duke Math. J. Volume 65, Number 1 (1992), 121-156.

First available in Project Euclid: 20 February 2004

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Digital Object Identifier

Primary: 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]
Secondary: 46M35: Abstract interpolation of topological vector spaces [See also 46B70] 47D99: None of the above, but in this section


Cobos, Fernando; Kühn, Thomas; Peetre, Jaak. Schatten-von Neumann classes of multilinear forms. Duke Math. J. 65 (1992), no. 1, 121--156. doi:10.1215/S0012-7094-92-06505-7. http://projecteuclid.org/euclid.dmj/1077295020.

Export citation


  • [1] J. Bergh, On the relation between the two complex methods of interpolation, Indiana Univ. Math. J. 28 (1979), no. 5, 775–778.
  • [2] J. Bergh and J. Löfström, Interpolation spaces. An introduction, Springer-Verlag, Berlin, 1976.
  • [3] A.-P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113–190.
  • [4] M. Cwikel and Y. Sagher, Relations between real and complex interpolation spaces, Indiana Univ. Math. J. 36 (1987), no. 4, 905–912.
  • [5] I. C. Gohberg and M. G. Kreĭ n, Introduction to the theory of linear nonselfadjoint operators, Translated from the Russian by A. Feinstein. Translations of Mathematical Monographs, Vol. 18, Amer. Math. Soc., Providence, R.I., 1969.
  • [6] S. Janson, J. Peetre, and R. Rochberg, Hankel forms and the Fock space, Rev. Mat. Iberoamericana 3 (1987), no. 1, 61–138.
  • [7] C. Jordan, Réduction d'un réseau de formes quadratiques ou bilinéaires, Première Partie, J. Math. Pures Appl. 2 (1906), 403–438, Deuxième Partie, 3 (1907), 5–51. Reprinted in Oeuvres, III, Gauthier-Villars, Paris, 1962, 269–350.
  • [8] J.-L. Lions and J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Études Sci. Publ. Math. (1964), no. 19, 5–68.
  • [9] J. Peetre, Sur la transformation de Fourier des fonctions à valeurs vectorielles, Rend. Sem. Mat. Univ. Padova 42 (1969), 15–26.
  • [10] J. Peetre, Paracommutators and minimal spaces, Operators and function theory (Lancaster, 1984), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 153, Reidel, Dordrecht, 1985, pp. 163–224.
  • [11] J. Peetre, Paracommutators—brief introduction, open problems, Rev. Mat. Univ. Complut. Madrid 2 (1989), no. suppl., 201–211.
  • [12] A. Pietsch, Ideals of multilinear functionals (designs of a theory), Proceedings of the second international conference on operator algebras, ideals, and their applications in theoretical physics (Leipzig, 1983), Teubner-Texte Math., vol. 67, Teubner, Leipzig, 1984, pp. 185–199.
  • [13] A. Pietsch, Eigenvalues and $s$-numbers, Cambridge Studies in Advanced Mathematics, vol. 13, Cambridge University Press, Cambridge, 1987.
  • [14] B. Simon, Trace ideals and their applications, London Mathematical Society Lecture Note Series, vol. 35, Cambridge University Press, Cambridge, 1979.
  • [15] H. Triebel, Interpolation theory, function spaces, differential operators, North-Holland Mathematical Library, vol. 18, North-Holland Publishing Co., Amsterdam, 1978.