An alternative Dunford-Pettis Property

Walden Freedman

Studia Mathematica (1997)

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

Abstract

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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.

How to cite

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Freedman, 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

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  3. [3] C. Chu and B. Iochum, The Dunford-Pettis property in C*-algebras, Studia Math. 97 (1990), 59-64. Zbl0734.46034
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  7. [7] J. Diestel, Sequences and Series in Banach Spaces, Springer, New York, 1984. 
  8. [8] J. Diestel, A survey of results related to the Dunford-Pettis property, in: Contemp. Math. 2, Amer. Math. Soc., 1980, 15-60. 
  9. [9] J. Diestel, Remarks on weak compactness in L 1 ( μ , X ) , Glasgow Math. J. 18 (1977), 87-91. 
  10. [10] R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras I, Academic Press, 1983. Zbl0518.46046
  11. [11] E. J. McShane, Linear functionals on certain Banach spaces, Proc. Amer. Math. Soc. 11 (1950), 402-408. Zbl0039.11802
  12. [12] M. Takesaki, Theory of Operator Algebras I, Springer, New York, 1979. 
  13. [13] J. Tomiyama, A characterization of C*-algebras whose conjugate spaces are separable, Tôhoku Math. J. 15 (1963), 96-102. Zbl0161.11004
  14. [14] P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge Stud. Adv. Math. 25, Cambridge Univ. Press, 1991. Zbl0724.46012

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