Title:
|
Some remarks on the equality $W(E,F^\ast) = K(E,F^\ast)$ (English) |
Author:
|
Emmanuele, G. |
Language:
|
English |
Journal:
|
Archivum Mathematicum |
ISSN:
|
0044-8753 (print) |
ISSN:
|
1212-5059 (online) |
Volume:
|
34 |
Issue:
|
4 |
Year:
|
1998 |
Pages:
|
417-425 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
We show that the equality $W(E,F^\ast )=K(E,F^\ast )$ is a necessary condition for the validity of certain results about isomorphic properties in the projective tensor product $E \otimes _\pi F$ of two Banach spaces under some approximation property type assumptions. (English) |
Keyword:
|
operator spaces |
Keyword:
|
isomorphic properties |
Keyword:
|
approximation properties |
MSC:
|
46B03 |
MSC:
|
46B20 |
MSC:
|
46B28 |
idZBL:
|
Zbl 0970.46011 |
idMR:
|
MR1679636 |
. |
Date available:
|
2009-02-17T10:15:40Z |
Last updated:
|
2012-05-10 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107669 |
. |
Reference:
|
[D] Diestel, J.: A survey of results related to the Dunford-Pettis property.Contemporary Math. 2, Amer. Math. Soc. 1980. Zbl 0571.46013, MR 0621850 |
Reference:
|
[E1] Emmanuele, G.: About certain isomorphic properties of Banach spaces in projective tensor products.Extract Math. 5 (1990) 23-25. |
Reference:
|
[E2] Emmanuele, G.: On the Reciprocal Dunford-Pettis property in projective tensor products.Math. Proc. Cambridge Phil. Soc. 109 (1991) 161-166. Zbl 0752.46042, MR 1075128 |
Reference:
|
[E3] Emmanuele, G.: On Banach spaces with the property (V$^\ast $) of Pelczynski, II.Annali Mat. Pura Appl. 160 (1991) 163-170. MR 1163206 |
Reference:
|
[E4] Emmanuele, G.: A remark on the containment of $c_0$ in spaces of compact operators.Math. Proc. Cambridge Phil. Soc. 111 (1992) 331-335. MR 1142753 |
Reference:
|
[E5] Emmanuele, G.: Banach spaces in which Dunford-Pettis sets are relatively compact.Archiv Math. 58 (1992) 477-485. Zbl 0761.46010, MR 1156580 |
Reference:
|
[EH] Emmanuele, G., Hensgen, W.: Property (V) of Pelczynski in projective tensor products.Proc. Royal Irish Acad. 95A,2 (1995) 227-231. MR 1660381 |
Reference:
|
[EJ] Emmanuele, G., John, K.: Uncomplementability of spaces of compact operators in larger spaces of operators.Czechoslovak Math. J., to appear. MR 1435603 |
Reference:
|
[F] Feder, M.: On subspaces of spaces with an unconditional basis and spaces of operators.Illinois J. Math. 24 (1980) 196-205. Zbl 0411.46009, MR 0575060 |
Reference:
|
[GJ] Ghoussoub, N., Johnson, W. B.: Factoring operators through Banach lattices not containing $C(0,1)$.Math. Z. 194 (1987) 153-171. MR 0876227 |
Reference:
|
[GG] Gonzalez, M., Gutierrez, J.: Polynomial Grothendieck property.preprint 1994. MR 1289296 |
Reference:
|
[HM] Heinrich, S., Mankiewicz, P.: Applications of ultrapowers to the uniform and Lipschitz classification of Banach spaces.Studia Math. 73 (1982) 215-251. MR 0675426 |
Reference:
|
[J] John, K.: On the uncomplemented subspace $K(X,Y)$.Czechoslovak Math. J. 42 (1992) 167-173. Zbl 0776.46016, MR 1152178 |
Reference:
|
[K] Kalton, N.: Spaces of compact operators.Math. Annalen 208 (1974) 267-278. Zbl 0266.47038, MR 0341154 |
Reference:
|
[Le] D.Lewis: Conditional weak compactness in certain inductive tensor products.Math. Annalen 201 (1973) 201-209. Zbl 0234.46069, MR 0326417 |
Reference:
|
[LT,I] Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces, Sequence Spaces.EMG 92, Springer Verlag 1977. MR 0500056 |
Reference:
|
[LT,II] Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces, Function Spaces.EMG 97, Springer Verlag 1979. MR 0540367 |
Reference:
|
[Lu] Lust, F.: Produits tensoriels projectifs d’espaces de Banach.Colloquium Math. 36 (1976) 255-267. Zbl 0356.46058, MR 0438153 |
Reference:
|
[R] Ruess, W.: Duality and geometry of spaces of operators, in Functional Analysis: Surveys and Recent Results, III.Math. Studies 90, North Holland 1984. MR 0761373 |
Reference:
|
[Se] Sersouri, A.: Propriété (u) dans les espaces d’opérateurs.Bull. Acad. Pol. Sci. 36 (1988) 655-659. Zbl 0622.46007, MR 1757565 |
Reference:
|
[Sz] Szankowski, A.: Subspaces without the approximation property.Israel J. Math. 30 (1978) 123-129. Zbl 0384.46008, MR 0508257 |
Reference:
|
[W] Willis, G.: The compact approximation property does not imply the approximation property.Studia Math. 103 (1992) 99-108. Zbl 0814.46017, MR 1184105 |
. |