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Ukrainian Mathematical Journal

, Volume 65, Issue 4, pp 649–655 | Cite as

Strongly alternative Dunford–Pettis subspaces of operator ideals

  • S. M. Moshtaghioun
Article
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Introducing the concept of strong alternative Dunford–Pettis property (strong DP1) for the subspace \( \mathcal{M} \) of operator ideals \( \mathcal{U} \)(X, Y) between Banach spaces X and Y, we show that \( \mathcal{M} \) is a strong DP1 subspace if and only if all evaluation operators \( {\phi_x}:\mathcal{M}\to Y \) and \( {\psi_{{{y^{*}}}}}:\mathcal{M}\to {X^{*}} \) are DP1 operators, where ϕ x (T) = Tx and ψ y* (T) = T*y* for xX, y*Y*, and T\( \mathcal{M} \). Some consequences related to the concept of alternative Dunford–Pettis property in the subspaces of some operator ideals are obtained.

Keywords

Banach Space Operator Ideal Linear Subspace Compact Operator Closed Subspace 
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References

  1. 1.
    L. Bunce and A. M. Peralta, “The alternative Dunford–Pettis property in C*-algebras and von Neumann preduals,” Proc. Amer. Math. Soc., 131, 1251–1255 (2002).MathSciNetCrossRefGoogle Scholar
  2. 2.
    C. H. Chu and B. Iochum, “The Dunford–Pettis property in C*-algebras,” Stud. Math., 97, 59–64 (1990).MathSciNetzbMATHGoogle Scholar
  3. 3.
    A. Defant and K. Floret, “Tensor norms and operator ideals,” Math. Stud., 179 (1993).Google Scholar
  4. 4.
    J. Diestel, “A survey of results related to the Dunford–Pettis property,” Contemp. Math., 2, 15–60 (1980).MathSciNetCrossRefGoogle Scholar
  5. 5.
    J. Diestel, “Sequences and series in Banach spaces,” Grad. Texts Math., 92 (1984).Google Scholar
  6. 6.
    W. Freedman, “An alternative Dunford–Pettis property,” Stud. Math., 125, 143–159 (1997).zbMATHGoogle Scholar
  7. 7.
    J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, II, Springer-Verlag, Berlin (1996).Google Scholar
  8. 8.
    S. M. Moshtaghioun, “The alternative Dunford–Pettis property in subspaces of operator ideals,” Bull. Korean Math. Soc., 47, No. 4, 743–750 (2010).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    S. M. Moshtaghioun, “Weakly completely continuous subspaces of operator ideals,” Taiwan. J. Math., 11, No. 2, 523–530 (2007).MathSciNetzbMATHGoogle Scholar
  10. 10.
    S. M. Moshtaghioun and J. Zafarani, “Completely continuous subspaces of operator ideals,” Taiwan. J. Math., 10, No. 3, 691–698 (2006).MathSciNetzbMATHGoogle Scholar
  11. 11.
    S. M. Moshtaghioun and J. Zafarani, “Weak sequential convergence in the dual of operator ideals,” J. Operator Theory, 49, 143–151 (2003).MathSciNetzbMATHGoogle Scholar
  12. 12.
    A. Pietsch, “Operator ideals,” North-Holland Math. Libr., 20 (1980).Google Scholar
  13. 13.
    A. Ülger, “Subspaces and subalgebras of K(H) whose duals have the Schur property,” J. Operator Theory, 37, 371–378 (1997).MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • S. M. Moshtaghioun
    • 1
  1. 1.Yazd UniversityYazdIran

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