| Title:
|
Complemented copies of $\ell_p$ spaces in tensor products (English) |
| Author:
|
Cilia, Raffaella |
| Author:
|
Gutiérrez, Joaquín M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
319-329 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\ell _p$. (English) |
| Keyword:
|
$\ell _p$ space |
| Keyword:
|
injective and projective tensor product |
| MSC:
|
46B20 |
| MSC:
|
46B28 |
| idZBL:
|
Zbl 1174.46009 |
| idMR:
|
MR2309967 |
| . |
| Date available:
|
2009-09-24T11:45:53Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128173 |
| . |
| Reference:
|
[1] J. Bourgain: New classes of ${L}_p$-spaces. Lecture Notes in Math.vol. 889, Springer, Berlin, 1981. MR 0639014 |
| Reference:
|
[2] J. Bourgain: New Banach space properties of the disc algebra and $H^\infty $.Acta Math. 152 (1984), 1–48. MR 0736210, 10.1007/BF02392189 |
| Reference:
|
[3] F. Cabello, D. Pérez-García and I. Villanueva: Unexpected subspaces of tensor products.J. London Math. Soc. 74 (2006), 512–526. MR 2269592 |
| Reference:
|
[4] J. M. F. Castillo: On Banach spaces $X$ such that ${\mathcal{L}}(L_p,X)={\mathcal{K}}(L_p,X)$.Extracta Math. 10 (1995), 27–36. MR 1359589 |
| Reference:
|
[5] A. Defant and K. Floret: Tensor Norms and Operator Ideals.Math. Studies 176, North-Holland, Amsterdam, 1993. MR 1209438 |
| Reference:
|
[6] J. Diestel: 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. Zbl 0571.46013, MR 0621850 |
| Reference:
|
[7] J. Diestel: Sequences and Series in Banach Spaces.Graduate Texts in Math. 92, Springer, Berlin, 1984. MR 0737004 |
| Reference:
|
[8] J. Diestel, H. Jarchow and A. Tonge: Absolutely Summing Operators.Cambridge Stud. Adv. Math. 43, Cambridge University Press, Cambridge, 1995. MR 1342297 |
| Reference:
|
[9] J. Diestel and J. J. Uhl, Jr.: Vector Measures.Math. Surveys Monographs 15, American Mathematical Society, Providence RI, 1977. MR 0453964 |
| Reference:
|
[10] E. Dubinsky, A. Pełczyński and H. P. Rosenthal: On Banach spaces $X$ for which $\Pi _2({L}_\infty ,X)=B({L}_\infty ,X)$.Studia Math. 44 (1972), 617–648. MR 0365097 |
| Reference:
|
[11] M. González and J. M. Gutiérrez: The Dunford-Pettis property on tensor products.Math. Proc. Cambridge Philos. Soc. 131 (2001), 185–192. MR 1833082 |
| Reference:
|
[12] J. M. Gutiérrez: Complemented copies of $\ell _2$ in spaces of integral operators.Glasgow Math. J. 47 (2005), 287–290. MR 2203495, 10.1017/S0017089505002491 |
| Reference:
|
[13] J. Lindenstrauss and A. Pełczyński: Absolutely summing operators in ${L}_p$-spaces and their applications.Studia Math. 29 (1968), 275–326. MR 0231188, 10.4064/sm-29-3-275-326 |
| Reference:
|
[14] J. Lindenstrauss and H. P. Rosenthal: The ${L}_p$-spaces.Israel J. Math. 7 (1969), 325–349. MR 0270119 |
| Reference:
|
[15] F. Lust: Produits tensoriels injectifs d’espaces de Sidon.Colloq. Math. 32 (1975), 285–289. Zbl 0306.46026, MR 0390794, 10.4064/cm-32-2-285-289 |
| Reference:
|
[16] H. P. Rosenthal: Point-wise compact subsets of the first Baire class.Amer. J. Math. 99 (1977), 362–378. Zbl 0392.54009, MR 0438113, 10.2307/2373824 |
| Reference:
|
[17] R. A. Ryan: The Dunford-Pettis property and projective tensor products.Bull. Polish Acad. Sci. Math. 35 (1987), 785–792. Zbl 0656.46057, MR 0961717 |
| Reference:
|
[18] M. Talagrand: Cotype of operators from $C(K)$.Invent. Math. 107 (1992), 1–40. Zbl 0788.47022, MR 1135462, 10.1007/BF01231879 |
| . |
