An alternative to the Dunford-Pettis Property, called the DP1-property, is introduced. Its relationship to the Dunford-Pettis Property and other related properties is examined. It is shown that -direct sums of spaces with DP1 have DP1 if 1 ≤ p < ∞. It is also shown that for preduals of von Neumann algebras, DP1 is strictly weaker than the Dunford-Pettis Property, while for von Neumann algebras, the two properties are equivalent.
@article{bwmeta1.element.bwnjournal-article-smv125i2p143bwm,
author = {Walden Freedman},
title = {An alternative Dunford-Pettis Property},
journal = {Studia Mathematica},
volume = {122},
year = {1997},
pages = {143-159},
zbl = {0897.46009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv125i2p143bwm}
}
Freedman, Walden. An alternative Dunford-Pettis Property. Studia Mathematica, Tome 122 (1997) pp. 143-159. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv125i2p143bwm/
[00000] [1] C. A. Akemann, Sequential convergence in the dual of a W*-algebra, Comm. Math. Phys. 7 (1968), 222-224.
[00001] [2] L. J. Bunce, The Dunford-Pettis property in the predual of a von Neumann algebra, Proc. Amer. Math. Soc. 116 (1992), 99-100. | Zbl 0810.46060
[00002] [3] C. Chu and B. Iochum, The Dunford-Pettis property in C*-algebras, Studia Math. 97 (1990), 59-64. | Zbl 0734.46034
[00003] [4] J. B. Conway, A Course in Functional Analysis, Springer, New York, 1985. | Zbl 0558.46001
[00004] [5] W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński, Factoring weakly compact operators, J. Funct. Anal. 17 (1974), 311-327. | Zbl 0306.46020
[00005] [6] G. F. Dell'Antonio, On the limits of sequences of normal states, Comm. Pure Appl. Math. 20 (1967), 413-429.
[00006] [7] J. Diestel, Sequences and Series in Banach Spaces, Springer, New York, 1984.
[00007] [8] J. Diestel, A survey of results related to the Dunford-Pettis property, in: Contemp. Math. 2, Amer. Math. Soc., 1980, 15-60.
[00008] [9] J. Diestel, Remarks on weak compactness in , Glasgow Math. J. 18 (1977), 87-91.
[00009] [10] R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras I, Academic Press, 1983. | Zbl 0518.46046
[00010] [11] E. J. McShane, Linear functionals on certain Banach spaces, Proc. Amer. Math. Soc. 11 (1950), 402-408. | Zbl 0039.11802
[00011] [12] M. Takesaki, Theory of Operator Algebras I, Springer, New York, 1979.
[00012] [13] J. Tomiyama, A characterization of C*-algebras whose conjugate spaces are separable, Tôhoku Math. J. 15 (1963), 96-102. | Zbl 0161.11004
[00013] [14] P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge Stud. Adv. Math. 25, Cambridge Univ. Press, 1991. | Zbl 0724.46012