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1995-1996 | 117 | 1 | 43-55
Tytuł artykułu

Extension of operators from weak*-closed sub-spaces of $l_1$ into C(K) spaces

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Abstrakty
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It is proved that every operator from a weak*-closed subspace of $ℓ_1$ into a space C(K) of continuous functions on a compact Hausdorff space K can be extended to an operator from $ℓ_1$ to C(K).
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Twórcy
  • Department of Mathematics, Texas A&M University, College Station, Texas 77843, U.S.A., johnson@math.tamu.edu
autor
Bibliografia
  • [Ami] D. Amir, Continuous function spaces with the separable projection property, Bull. Res. Council Israel 10F (1962), 163-164.
  • [BePe] C. Bessaga and A. Pełczyński, Spaces of continuous functions IV, Studia Math. 19 (1960), 53-62.
  • [BP] E. Bishop and R. R. Phelps, A proof that every Banach space is subreflexive, Bull. Amer. Math. Soc. 67 (1961), 97-98.
  • [Bou] N. Bourbaki, General Topology, Part 1, Addison-Wesley, 1966.
  • [Die] J. Diestel, Geometry of Banach Spaces - Selected Topics, Lecture Notes in Math. 485, Springer, 1975.
  • [Joh] W. B. Johnson, Factoring compact operators, Israel J. Math. 9 (1971), 337-345.
  • [JR] W. B. Johnson and H. P. Rosenthal, On w*-basic sequences and their applications to the study of Banach spaces, Studia Math. 43 (1972), 77-92.
  • [JRZ] W. B. Johnson, H. P. Rosenthal and M. Zippin, On bases, finite dimensional decompositions, and weaker structures in Banach spaces, Israel J. Math. 9 (1971), 488-506.
  • [JZ1] W. B. Johnson and M. Zippin, On subspaces of quotients of $(∑ G)_ℓ_p$ and $(∑ G)_c_0$, ibid. 13 (1972), 311-316.
  • [JZ2] W. B. Johnson and M. Zippin, Extension of operators from subspaces of $c_0(γ)$ into C(K) spaces, Proc. Amer. Math. Soc. 107 (1989), 751-754.
  • [Lin] J. Lindenstrauss, Extension of compact operators, Mem. Amer. Math. Soc. 48 (1964).
  • [LP] J. Lindenstrauss and A. Pełczyński, Contributions to the theory of the classical Banach spaces, J. Funct. Anal. 8 (1971), 225-249.
  • [LR] J. Lindenstrauss and H. P. Rosenthal, Automorphisms in $c_0$, $ℓ_1$, and m, Israel J. Math. 7 (1969), 227-239.
  • [LT1] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I. Sequence Spaces, Springer, 1977.
  • [LT2] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II. Function Spaces, Springer, 1979.
  • [Mac] G. Mackey, Note on a theorem of Murray, Bull. Amer. Math. Soc. 52 (1046), 322-325.
  • [Peł] A. Pełczyński, Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basis, Studia Math. 40 (1971), 239-242.
  • [Sam1] D. Samet, Vector measures are open maps, Math. Oper. Res. 9 (1984), 471-474.
  • [Sam2] D. Samet, Continuous selections for vector measures, ibid. 12 (1987), 536-543.
  • [Zip] M. Zippin, A global approach to certain operator extension problems, in: Longhorn Notes, Lecture Notes in Math. 1470, Springer, 1991, 78-84.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv117i1p43bwm
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