Hiroshima Mathematical Journal

$(p,\,q)$-nuclear and $(p,\,q)$-integral operators

Kenichi Miyazaki

Full-text: Open access

Article information

Source
Hiroshima Math. J., Volume 4, Number 1 (1974), 99-132.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206137156

Digital Object Identifier
doi:10.32917/hmj/1206137156

Mathematical Reviews number (MathSciNet)
MR0350482

Zentralblatt MATH identifier
0283.47015

Subjects
Primary: 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]

Citation

Miyazaki, Kenichi. $(p,\,q)$-nuclear and $(p,\,q)$-integral operators. Hiroshima Math. J. 4 (1974), no. 1, 99--132. doi:10.32917/hmj/1206137156. https://projecteuclid.org/euclid.hmj/1206137156


Export citation

References

  • [1] P. L. Butzer and H. Berens, Semi-groups of operators andapproximation, Grundlehren der Mathematische Wissenschaften Bd. 145, Springer, Berlin/Heidelberg/New York, 1967.
  • [2] A. Grothendieck, Produits tensoriels topologiques et espaces nucleaires, Mem. Amer. Math. Soc. 16, 1955.
  • [3] G. H. Hardy,J. E. Littlewood and G. Plya, Inequalities, Cambridge Univ. Press, 1967.
  • [4] T. Holmstedt, Interpolation of quasi-normed spaces, Math. Scand. 26 (1970), 177-199.
  • [5] J. R. Holub, A characterization of subspaces of L, Studia Math. 42 (1972), 265-270.
  • [6] R. Hunt, On L(p, q) spaces,Enseignement Math. 12 (1966), 249-276.
  • [7] S. Kwapie, Some remarks on (p, q)-absolutely summingoperators in lp -spaces,Studia Math. 29 (1968), 327-337.
  • [8] K. Miyazaki, (p, q; r)-absolutely summing operators, J. Math. Soc. Japan 24 (1972), 341- 354.
  • [9] L. Nachbin, Some problems in extending and lifting continuouslinear transformations, Proc. Internat. Sympos. Linear Spaces, Jerusalem Academic Press, Jerusalen (1961), 340-350.
  • [10] A. Persson, On some properties of p-nuclear andp-integral operators, Studia Math. 33 (1969), 213-222.
  • [11] A. Persson, A. Pietsch, p-nukleare und p-integrale Abbildungen in Banachrumen, Studia Math. 33 (1969), 19-62.
  • [12] A. Pietsch, Nuclear locally convexspaces,Ergebnisse der Mathematik Bd. 66, Springer, Berlin/Heidelberg/New York, 1972.
  • [13] A. Pietsch, Nuclear locally convexspaces, Absolut p-summierende Abbildungen in normiertenRumen, Studia Math. 28 (1967), 333-353.
  • [14] L. Schwartz, Produits tensoriels topologiques d'espaces vectoriels topologiques. Espaces vectoriels topologiques nucleaires.Applications, Seminaire Schwartz de la Faculte des Sciences de Paris, 1953/1954.
  • [15] K. Yoshinaga, Lorentz spaces and the Caldern-Zygmund theorem, Bull. Kyushu Inst. Tech. 16 (1969), 1-38.