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A remark on the containment of c0 in spaces of compact operators

Published online by Cambridge University Press:  24 October 2008

G. Emmanuele
G. Emmanuele
Affiliation:
Department of Mathematics, University of Catania, Viale A. Doria, 6-95125 Catania, Italy
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Extract

Let X, Y be two Banach spaces. By L(X, Y) (resp. K(X, Y)) we denote the Banach space of all bounded, linear (resp. compact, bounded, linear) operators from X into Y. Several papers have been devoted to the question of when c0 embeds isomorphically into K(X, Y) (see 5, 8, 9 and their references) and its relationship with the following question:

(i) is K(X, Y) always uncomplemented in L(X, Y) when L(X, Y)K(X, Y)?

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 2 , March 1992 , pp. 331 - 335
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

REFERENCES

1Diestel, J. and Uhl, J. J. Jr. Vector Measures. Math. Surveys no. 15 (American Mathematical Society, 1977).CrossRefGoogle Scholar
2Diestel, J. and Uhl, J. J. Jr. Progress in Vector Measures, 197783. Lecture Notes in Math. vol. 1033 (Springer-Verlag, 1983).Google Scholar
3Diestel, J.. Sequences and Series in Banach Spaces. Graduate Texts in Math. no. 92 (Springer-Verlag, 1984).CrossRefGoogle Scholar
4Emmanuele, G.. On the containment of c 0 by spaces of compact operators. Bull. Sci. Math. (2) 115 (1991), 177184.Google Scholar
5Feder, M.. On subspaces of spaces with an unconditional basis and spaces of operators. Illinois J. Math. 34 (1980), 196205.Google Scholar
6Feder, M.. On the nonexistence of a projection onto the space of compact operators. Canad. Math. Bull. 25, (1982), 7881.CrossRefGoogle Scholar
7Holub, J. R.. Tensor product bases and tensor diagonals. Trans. Amer. Math. Soc. 151 (1970), 563579.CrossRefGoogle Scholar
8Johnson, J.. Remarks on Banach spaces of compact operators. J. Fund. Anal. 32 (1979), 304311.CrossRefGoogle Scholar
9Kalton, N. J.. Spaces of compact operators. Math. Ann. 208 (1974), 267278.CrossRefGoogle Scholar
10Pelczynski, A.. On Banach spaces containing L l(). Studia Math. 30 (1968), 231246.CrossRefGoogle Scholar
11Schlumprecht, T.. Limited sets in Banach spaces. Doktorarbeit, Universitt Mnchen (1987).Google Scholar
12Bourgain, J. and Delbaen, F.. A class of special L-spaces. Acta Math. 145 (1980), 155176.CrossRefGoogle Scholar