Complemented copies of ℓ p spaces in tensor products

Raffaella Cilia; Joaquín M. Gutiérrez

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 1, page 319-329
  • ISSN: 0011-4642

Abstract

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We give sufficient conditions on Banach spaces X and Y so that their projective tensor product X ⊗ π Y , their injective tensor product X ⊗ ϵ Y , or the dual ( X ⊗ π Y ) * contain complemented copies of ℓ p .

How to cite

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Cilia, Raffaella, and Gutiérrez, Joaquín M.. "Complemented copies of $\ell _p$ spaces in tensor products." Czechoslovak Mathematical Journal 57.1 (2007): 319-329. <http://eudml.org/doc/31131>.

@article{Cilia2007,
abstract = {We give sufficient conditions on Banach spaces $X$ and $Y$ so that their projective tensor product $X\otimes _\pi Y$, their injective tensor product $X\otimes _\epsilon Y$, or the dual $(X\otimes _\pi Y)^*$ contain complemented copies of $\ell _p$.},
author = {Cilia, Raffaella, Gutiérrez, Joaquín M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {$\ell _p$ space; injective and projective tensor product; space; injective and projective tensor product},
language = {eng},
number = {1},
pages = {319-329},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Complemented copies of $\ell _p$ spaces in tensor products},
url = {http://eudml.org/doc/31131},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Cilia, Raffaella
AU - Gutiérrez, Joaquín M.
TI - Complemented copies of $\ell _p$ spaces in tensor products
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 319
EP - 329
AB - We give sufficient conditions on Banach spaces $X$ and $Y$ so that their projective tensor product $X\otimes _\pi Y$, their injective tensor product $X\otimes _\epsilon Y$, or the dual $(X\otimes _\pi Y)^*$ contain complemented copies of $\ell _p$.
LA - eng
KW - $\ell _p$ space; injective and projective tensor product; space; injective and projective tensor product
UR - http://eudml.org/doc/31131
ER -

References

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  1. New classes of L p -spaces. Lecture Notes in Math, vol. 889, Springer, Berlin, 1981. (1981) MR0639014
  2. 10.1007/BF02392189, Acta Math. 152 (1984), 1–48. (1984) MR0736210DOI10.1007/BF02392189
  3. Unexpected subspaces of tensor products, J. London Math. Soc. 74 (2006), 512–526. (2006) MR2269592
  4. On Banach spaces X such that ℒ ( L p , X ) = 𝒦 ( L p , X ) , Extracta Math. 10 (1995), 27–36. (1995) MR1359589
  5. Tensor Norms and Operator Ideals, Math. Studies 176, North-Holland, Amsterdam, 1993. (1993) MR1209438
  6. A survey of results related to the Dunford-Pettis property, In: W. H. Graves (ed.), Proc. Conf. on Integration, Topology and Geometry in Linear Spaces, Chapel Hill 1979, Contemp. Math. 2, 15–60, American Mathematical Society, Providence RI, 1980. Zbl0571.46013MR0621850
  7. Sequences and Series in Banach Spaces, Graduate Texts in Math. 92, Springer, Berlin, 1984. (1984) MR0737004
  8. Absolutely Summing Operators, Cambridge Stud. Adv. Math. 43, Cambridge University Press, Cambridge, 1995. (1995) MR1342297
  9. Vector Measures, Math. Surveys Monographs 15, American Mathematical Society, Providence RI, 1977. (1977) MR0453964
  10. On Banach spaces X for which Π 2 ( L ∞ , X ) = B ( L ∞ , X ) , Studia Math. 44 (1972), 617–648. (1972) MR0365097
  11. The Dunford-Pettis property on tensor products, Math. Proc. Cambridge Philos. Soc. 131 (2001), 185–192. (2001) MR1833082
  12. 10.1017/S0017089505002491, Glasgow Math. J. 47 (2005), 287–290. (2005) MR2203495DOI10.1017/S0017089505002491
  13. 10.4064/sm-29-3-275-326, Studia Math. 29 (1968), 275–326. (1968) MR0231188DOI10.4064/sm-29-3-275-326
  14. The L p -spaces, Israel J. Math. 7 (1969), 325–349. (1969) MR0270119
  15. 10.4064/cm-32-2-285-289, Colloq. Math. 32 (1975), 285–289. (1975) Zbl0306.46026MR0390794DOI10.4064/cm-32-2-285-289
  16. 10.2307/2373824, Amer. J. Math. 99 (1977), 362–378. (1977) Zbl0392.54009MR0438113DOI10.2307/2373824
  17. The Dunford-Pettis property and projective tensor products, Bull. Polish Acad. Sci. Math. 35 (1987), 785–792. (1987) Zbl0656.46057MR0961717
  18. 10.1007/BF01231879, Invent. Math. 107 (1992), 1–40. (1992) Zbl0788.47022MR1135462DOI10.1007/BF01231879

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