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

• Autorzy: W. B. Johnson , M. Zippin
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46B15: Summability and bases

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995-1996
• Tom: 117
• Numer: 1
• Strony: 43-55

Daty

wydano

1994-12-16

poprawiono

1995-07-04

Twórcy

autor

W. B. Johnson

• Department of Mathematics, Texas A&M University, College Station, Texas 77843, U.S.A.,

autor

M. Zippin

• Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel,

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.