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operator spaces; isomorphic properties; approximation properties
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.
[D] Diestel, J.: A survey of results related to the Dunford-Pettis property. Contemporary Math. 2, Amer. Math. Soc. 1980. MR 0621850 | Zbl 0571.46013
[E1] Emmanuele, G.: About certain isomorphic properties of Banach spaces in projective tensor products. Extract Math. 5 (1990) 23-25.
[E2] Emmanuele, G.: On the Reciprocal Dunford-Pettis property in projective tensor products. Math. Proc. Cambridge Phil. Soc. 109 (1991) 161-166. MR 1075128 | Zbl 0752.46042
[E3] Emmanuele, G.: On Banach spaces with the property (V$^\ast $) of Pelczynski, II. Annali Mat. Pura Appl. 160 (1991) 163-170. MR 1163206
[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
[E5] Emmanuele, G.: Banach spaces in which Dunford-Pettis sets are relatively compact. Archiv Math. 58 (1992) 477-485. MR 1156580 | Zbl 0761.46010
[EH] Emmanuele, G., Hensgen, W.: Property (V) of Pelczynski in projective tensor products. Proc. Royal Irish Acad. 95A,2 (1995) 227-231. MR 1660381
[EJ] Emmanuele, G., John, K.: Uncomplementability of spaces of compact operators in larger spaces of operators. Czechoslovak Math. J., to appear. MR 1435603
[F] Feder, M.: On subspaces of spaces with an unconditional basis and spaces of operators. Illinois J. Math. 24 (1980) 196-205. MR 0575060 | Zbl 0411.46009
[GJ] Ghoussoub, N., Johnson, W. B.: Factoring operators through Banach lattices not containing $C(0,1)$. Math. Z. 194 (1987) 153-171. MR 0876227
[GG] Gonzalez, M., Gutierrez, J.: Polynomial Grothendieck property. preprint 1994. MR 1289296
[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
[J] John, K.: On the uncomplemented subspace $K(X,Y)$. Czechoslovak Math. J. 42 (1992) 167-173. MR 1152178 | Zbl 0776.46016
[K] Kalton, N.: Spaces of compact operators. Math. Annalen 208 (1974) 267-278. MR 0341154 | Zbl 0266.47038
[Le] D.Lewis: Conditional weak compactness in certain inductive tensor products. Math. Annalen 201 (1973) 201-209. MR 0326417 | Zbl 0234.46069
[LT,I] Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces, Sequence Spaces. EMG 92, Springer Verlag 1977. MR 0500056
[LT,II] Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces, Function Spaces. EMG 97, Springer Verlag 1979. MR 0540367
[Lu] Lust, F.: Produits tensoriels projectifs d’espaces de Banach. Colloquium Math. 36 (1976) 255-267. MR 0438153 | Zbl 0356.46058
[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
[Se] Sersouri, A.: Propriété (u) dans les espaces d’opérateurs. Bull. Acad. Pol. Sci. 36 (1988) 655-659. MR 1757565 | Zbl 0622.46007
[Sz] Szankowski, A.: Subspaces without the approximation property. Israel J. Math. 30 (1978) 123-129. MR 0508257 | Zbl 0384.46008
[W] Willis, G.: The compact approximation property does not imply the approximation property. Studia Math. 103 (1992) 99-108. MR 1184105 | Zbl 0814.46017
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