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1997 | 125 | 2 | 143-159
Tytuł artykułu

An alternative Dunford-Pettis Property

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EN
Abstrakty
EN
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.
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Twórcy
  • Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106, U.S.A., freedman@perl.emu.edu.tr
  • Department of Mathematics, Eastern Mediterranean University, Gazimağusa, TRNC, Mersin 10, Turkey
Bibliografia
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  • [2] L. J. Bunce, The Dunford-Pettis property in the predual of a von Neumann algebra, Proc. Amer. Math. Soc. 116 (1992), 99-100.
  • [3] C. Chu and B. Iochum, The Dunford-Pettis property in C*-algebras, Studia Math. 97 (1990), 59-64.
  • [4] J. B. Conway, A Course in Functional Analysis, Springer, New York, 1985.
  • [5] W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński, Factoring weakly compact operators, J. Funct. Anal. 17 (1974), 311-327.
  • [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 $L_1(μ,X)$, 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.
  • [11] E. J. McShane, Linear functionals on certain Banach spaces, Proc. Amer. Math. Soc. 11 (1950), 402-408.
  • [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.
  • [14] P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge Stud. Adv. Math. 25, Cambridge Univ. Press, 1991.
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bwmeta1.element.bwnjournal-article-smv125i2p143bwm
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