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

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Abstract

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.

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References

  1. Bombal F., Pérez-García D., Villanueva I. (2004) Multilinear extensions of Grothendieck’s theorem. Q. J. Math 55: 441–450

    Article  MathSciNet  MATH  Google Scholar 

  2. Botelho G. et al (2009) Inclusions and coincidences for multiple summing multilinear mappings. Proc. Amer. Math. Soc 137: 991–1000

    Article  MathSciNet  MATH  Google Scholar 

  3. Botelho G., Michels C., Pellegrino D. (2010) Complex interpolation and summability properties of multilinear operators. Rev. Mat. Complut 23: 139–161

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Defant and K. Floret, Tensor norms and operator ideals, North-Holland, Math. Studies, 176, 1993.

  5. Defant A. et al (2008) Bohr’s strip for vector valued Dirichlet series. Math. Ann 342: 533–555

    Article  MathSciNet  MATH  Google Scholar 

  6. Defant A., Pérez-García D. (2008) A tensor norm preserving unconditionality for \({\mathcal{L}_{p}}\) -spaces. Trans. Amer. Math. Soc 360: 3287–3306

    Article  MathSciNet  MATH  Google Scholar 

  7. Defant A., Popa D., Schwarting U. (2010) Coordinatewise multiple summing operators in Banach spaces. J. Funct. Anal 259: 220–242

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Distel, H. Jarchow, and A. Tonge, Absolutely Summing Operators, Cambridge Stud. Adv. Math. 43, Cambridge University Press, 1995.

  9. S. Geiss, Ideale multilinearer Abbildungen, Diplomarbeit, 1984.

  10. Junek H., Matos M.C., Pellegrino D. (2008) Inclusion theorems for absolutely summing holomorphic mappings Proc. Amer. Math. Soc 136: 3983–3991

    Article  MathSciNet  MATH  Google Scholar 

  11. Matos M.C. (2003) Fully absolutely summing and Hilbert–Schmidt multilinear mappings. Collect. Math 54: 111–136

    MathSciNet  MATH  Google Scholar 

  12. B. Maurey, Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces Lp, Astérisque 11 (1974).

  13. Pérez-García D. (2004) The inclusion theorem for multiple summing operators. Studia Math 165: 275–290

    Article  MathSciNet  MATH  Google Scholar 

  14. Pérez-García D. (2005) Comparing different classes of absolutely summing multilinear operators. Arch. Math 85: 258–267

    Article  MATH  Google Scholar 

  15. Pérez-Garcí D. et al (2008) Unbounded violation of tripartite Bell inequalities. Comm. Math. Phys 279: 455–486

    Article  MathSciNet  Google Scholar 

  16. A. Pietsch, Operator ideals, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978; North Holland, 1980.

  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.

  18. Popa D. (2010) Multilinear variants of Maurey and Pietsch theorems and applications. J. Math. Anal. Appl 368: 157–168

    Article  MathSciNet  MATH  Google Scholar 

  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.

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Correspondence to Dumitru Popa.

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Popa, D. A new distinguishing feature for summing, versus dominated and multiple summing operators. Arch. Math. 96, 455–462 (2011). https://doi.org/10.1007/s00013-011-0258-x

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