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Grothendieck's property in Lp(μ, X)

Published online by Cambridge University Press:  18 May 2009

Santiago Díaz
Santiago Díaz
Affiliation:
Departamento de Mathematica Aplicada II, Universidad de Sevilla, Sevilla, Spain E-mail: madrigal@cica.es
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Abstract

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We prove that, for non purely atomic measures, Lp (μ, X) is a Grothendieck space if and only if X is reflexive.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 3 , September 1995, pp. 379 - 382
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

REFERENCES

1.Bombal, F., Operators on vector sequence spaces, London Mathematical Society Lecture Notes 140 (1989), 94–106.Google Scholar
2.Cembranos, P., C(K; E) contains a complemented copy of c0, Proc. Amer. Math. Soc. 91 (1984), 556–558.Google Scholar
3.Civin, P. and Yood, B., Quasireflexive spaces, Proc. Amer. Math. Soc. 8 (1957), 906–911.CrossRefGoogle Scholar
4.Conway, J. B., A Course in Functional Analysis (Springer-Verlag, 1990).Google Scholar
5.Diestel, J., Sequences and Series in Banach Spaces (Springer-Verlag, 1984).CrossRefGoogle Scholar
6.Diestel, J., Grothendieck spaces and vector measures in Vector and Operator Valued Measures and Applications (Proc. Sympos., Snowbird Resort, Alta, Utah, 1972), (Academic Press, 1973), 97–108.CrossRefGoogle Scholar
7.Diestel, J. and Uhl, J. J, Vector Measures, Math. Surveys, Amer. Math. Soc. 15 (1977).CrossRefGoogle Scholar
8.Emmanuele, G., On complemented copies of c0 in Lpx, 1 ≤ p, < ∞, Proc. Amer. Math. Soc. 104 (1988), 785–786.Google Scholar
9.Johnson, W. B., A complementary universal conjugate Banach space and its relation to the aproximation problem, Israel J. Math. 13 (1972), 301–310.CrossRefGoogle Scholar
10.Johnson, W. B. and Rosenthal, H. P., Onw*-basic sequences and their applications to the study of Banach spaces, Studia Math. 43 (1972), 77–92.CrossRefGoogle Scholar
11.Khurana, S. S., Grothendieck spaces, Illinois J. Math., 22 (1978), 79–80.CrossRefGoogle Scholar
12.Mendoza, J., Complemented copies of l1 in Lp (μ; E), Math. Proc. Camb. Phil. Soc. III (1992), 531–534.Google Scholar
13.Meyer-Nieberg, P., Banach Lattices (Springer-Verlag, 1991).CrossRefGoogle Scholar
14.Rosenthal, H. P., Pointwise compact subsets of the first Baire class, Amer. J. Math. 99 (1977), 362–378.CrossRefGoogle Scholar
15.Saab, E. and Saab, P., On stability problems of some properties in Banach spaces in Function Spaces, Lecture Notes in Pure and Appl. Math. 136 (Marcel Dekker, New York, 1992), 367–403.Google Scholar