Archiv der Mathematik

, 96:455 | Cite as

A new distinguishing feature for summing, versus dominated and multiple summing operators

  • Dumitru Popa


We prove results which show a new distinctive feature between the class of summing, versus dominated and multiple summing operators. We improve also some recent results in this area.

Mathematics Subject Classification (2000)

Primary 46G25 Secondary 46B25 46C99 


p-summing Multilinear operators 


  1. 1.
    Bombal F., Pérez-García D., Villanueva I. (2004) Multilinear extensions of Grothendieck’s theorem. Q. J. Math 55: 441–450MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Botelho G. et al (2009) Inclusions and coincidences for multiple summing multilinear mappings. Proc. Amer. Math. Soc 137: 991–1000MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Botelho G., Michels C., Pellegrino D. (2010) Complex interpolation and summability properties of multilinear operators. Rev. Mat. Complut 23: 139–161MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    A. Defant and K. Floret, Tensor norms and operator ideals, North-Holland, Math. Studies, 176, 1993.Google Scholar
  5. 5.
    Defant A. et al (2008) Bohr’s strip for vector valued Dirichlet series. Math. Ann 342: 533–555MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Defant A., Pérez-García D. (2008) A tensor norm preserving unconditionality for \({\mathcal{L}_{p}}\) -spaces. Trans. Amer. Math. Soc 360: 3287–3306MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Defant A., Popa D., Schwarting U. (2010) Coordinatewise multiple summing operators in Banach spaces. J. Funct. Anal 259: 220–242MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    J. Distel, H. Jarchow, and A. Tonge, Absolutely Summing Operators, Cambridge Stud. Adv. Math. 43, Cambridge University Press, 1995.Google Scholar
  9. 9.
    S. Geiss, Ideale multilinearer Abbildungen, Diplomarbeit, 1984.Google Scholar
  10. 10.
    Junek H., Matos M.C., Pellegrino D. (2008) Inclusion theorems for absolutely summing holomorphic mappings Proc. Amer. Math. Soc 136: 3983–3991MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Matos M.C. (2003) Fully absolutely summing and Hilbert–Schmidt multilinear mappings. Collect. Math 54: 111–136MathSciNetMATHGoogle Scholar
  12. 12.
    B. Maurey, Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces Lp, Astérisque 11 (1974).Google Scholar
  13. 13.
    Pérez-García D. (2004) The inclusion theorem for multiple summing operators. Studia Math 165: 275–290MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Pérez-García D. (2005) Comparing different classes of absolutely summing multilinear operators. Arch. Math 85: 258–267MATHCrossRefGoogle Scholar
  15. 15.
    Pérez-Garcí D. et al (2008) Unbounded violation of tripartite Bell inequalities. Comm. Math. Phys 279: 455–486MathSciNetCrossRefGoogle Scholar
  16. 16.
    A. Pietsch, Operator ideals, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978; North Holland, 1980.Google Scholar
  17. 17.
    A. Pietsch, Ideals of multilinear functionals, in: Proceedings of the Second International Conference on Operator Algebras, Ideals and Their Applications in Theoretical Physics, Teubner-Texte, Leipzig, 1983, 185–199.Google Scholar
  18. 18.
    Popa D. (2010) Multilinear variants of Maurey and Pietsch theorems and applications. J. Math. Anal. Appl 368: 157–168MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    N. Tomczak-Jagermann, Banach-Mazur distances and finite dimensional operator ideals, Pitman Monographs and Surveys in Pure and Applied Mathematics, 38, Harlow: Longman Scientific & Technical; New York: John Wiley & Sons, Inc., 1989.Google Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ConstantaConstantaRomania

Personalised recommendations