# An alternative Dunford-Pettis Property

Studia Mathematica (1997)

- Volume: 125, Issue: 2, page 143-159
- ISSN: 0039-3223

## Access Full Article

top## Abstract

top## How to cite

topFreedman, Walden. "An alternative Dunford-Pettis Property." Studia Mathematica 125.2 (1997): 143-159. <http://eudml.org/doc/216428>.

@article{Freedman1997,

abstract = {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 $ℓ_p$-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.},

author = {Freedman, Walden},

journal = {Studia Mathematica},

keywords = {Dunford-Pettis Property; Kadec-Klee Property; Kadec-Klee property; Dunford-Pettis property; DP1-property; preduals of von Neumann algebras},

language = {eng},

number = {2},

pages = {143-159},

title = {An alternative Dunford-Pettis Property},

url = {http://eudml.org/doc/216428},

volume = {125},

year = {1997},

}

TY - JOUR

AU - Freedman, Walden

TI - An alternative Dunford-Pettis Property

JO - Studia Mathematica

PY - 1997

VL - 125

IS - 2

SP - 143

EP - 159

AB - 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 $ℓ_p$-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.

LA - eng

KW - Dunford-Pettis Property; Kadec-Klee Property; Kadec-Klee property; Dunford-Pettis property; DP1-property; preduals of von Neumann algebras

UR - http://eudml.org/doc/216428

ER -

## References

top- [1] C. A. Akemann, Sequential convergence in the dual of a W*-algebra, Comm. Math. Phys. 7 (1968), 222-224.
- [2] L. J. Bunce, The Dunford-Pettis property in the predual of a von Neumann algebra, Proc. Amer. Math. Soc. 116 (1992), 99-100. Zbl0810.46060
- [3] C. Chu and B. Iochum, The Dunford-Pettis property in C*-algebras, Studia Math. 97 (1990), 59-64. Zbl0734.46034
- [4] J. B. Conway, A Course in Functional Analysis, Springer, New York, 1985. Zbl0558.46001
- [5] W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński, Factoring weakly compact operators, J. Funct. Anal. 17 (1974), 311-327. Zbl0306.46020
- [6] G. F. Dell'Antonio, On the limits of sequences of normal states, Comm. Pure Appl. Math. 20 (1967), 413-429.
- [7] J. Diestel, Sequences and Series in Banach Spaces, Springer, New York, 1984.
- [8] J. Diestel, A survey of results related to the Dunford-Pettis property, in: Contemp. Math. 2, Amer. Math. Soc., 1980, 15-60.
- [9] J. Diestel, Remarks on weak compactness in ${L}_{1}(\mu ,X)$, Glasgow Math. J. 18 (1977), 87-91.
- [10] R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras I, Academic Press, 1983. Zbl0518.46046
- [11] E. J. McShane, Linear functionals on certain Banach spaces, Proc. Amer. Math. Soc. 11 (1950), 402-408. Zbl0039.11802
- [12] M. Takesaki, Theory of Operator Algebras I, Springer, New York, 1979.
- [13] J. Tomiyama, A characterization of C*-algebras whose conjugate spaces are separable, Tôhoku Math. J. 15 (1963), 96-102. Zbl0161.11004
- [14] P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge Stud. Adv. Math. 25, Cambridge Univ. Press, 1991. Zbl0724.46012

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.