Grothendieck's property in Lp(μ, X)
Glasgow mathematical journal, Tome 37 (1995) no. 3, pp. 379-382

Voir la notice de l'article provenant de la source Cambridge University Press

We prove that, for non purely atomic measures, Lp (μ, X) is a Grothendieck space if and only if X is reflexive.
Díaz, Santiago. Grothendieck's property in Lp(μ, X). Glasgow mathematical journal, Tome 37 (1995) no. 3, pp. 379-382. doi: 10.1017/S0017089500031669
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[1] 1.Bombal, F., Operators on vector sequence spaces, London Mathematical Society Lecture Notes 140 (1989), 94–106. Google Scholar

[2] 2.Cembranos, P., C(K; E) contains a complemented copy of c, Proc. Amer. Math. Soc. 91 (1984), 556–558. Google Scholar

[3] 3.Civin, P. and Yood, B., Quasireflexive spaces, Proc. Amer. Math. Soc. 8 (1957), 906–911. Google Scholar | DOI

[4] 4.Conway, J. B., A Course in Functional Analysis (Springer-Verlag, 1990). Google Scholar

[5] 5.Diestel, J., Sequences and Series in Banach Spaces (Springer-Verlag, 1984). Google Scholar | DOI

[6] 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. Google Scholar | DOI

[7] 7.Diestel, J. and Uhl, J. J, Vector Measures, Math. Surveys, Amer. Math. Soc. 15 (1977). Google Scholar | DOI

[8] 8.Emmanuele, G., On complemented copies of c in Lp, 1 ≤ p, < ∞, Proc. Amer. Math. Soc. 104 (1988), 785–786. Google Scholar

[9] 9.Johnson, W. B., A complementary universal conjugate Banach space and its relation to the aproximation problem, Israel J. Math. 13 (1972), 301–310. Google Scholar | DOI

[10] 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. Google Scholar | DOI

[11] 11.Khurana, S. S., Grothendieck spaces, Illinois J. Math., 22 (1978), 79–80. Google Scholar | DOI

[12] 12.Mendoza, J., Complemented copies of l in Lp (μ; E), Math. Proc. Camb. Phil. Soc. III (1992), 531–534. Google Scholar

[13] 13.Meyer-Nieberg, P., Banach Lattices (Springer-Verlag, 1991). Google Scholar | DOI

[14] 14.Rosenthal, H. P., Pointwise compact subsets of the first Baire class, Amer. J. Math. 99 (1977), 362–378. Google Scholar | DOI

[15] 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

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