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1999 | 80 | 2 | 235-244
Tytuł artykułu

Mapping Properties of $c_0$

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Bessaga and Pełczyński showed that if $c_0$ embeds in the dual $X^*$ of a Banach space X, then $ℓ^1$ embeds as a complemented subspace of X. Pełczyński proved that every infinite-dimensional closed linear subspace of $ℓ^1$ contains a copy of $ℓ^1$ that is complemented in $ℓ^1$. Later, Kadec and Pełczyński proved that every non-reflexive closed linear subspace of $L^1 [0,1]$ contains a copy of $ℓ^1$ that is complemented in $L^1 [0,1]$. In this note a traditional sliding hump argument is used to establish a simple mapping property of $c_0$ which simultaneously yields extensions of the preceding theorems as corollaries. Additional classical mapping properties of $c_0$ are briefly discussed and applications are given.
Słowa kluczowe
Rocznik
Tom
80
Numer
2
Strony
235-244
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-11-10
Twórcy
autor
  • University of North Texas, Denton, Texas
Bibliografia
  • [1] C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151-164.
  • [2] J. Brooks and N. Dinculeanu, Strong additivity, absolute continuity, and compactness in spaces of measures, J. Math. Anal. Appl. 45 (1974), 156-175.
  • [3] J. Diestel, Sequences and Series in Banach Spaces, Grad. Texts in Math. 92, Springer, New York, 1984.
  • [4] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, 1977.
  • [5] N. Dunford, A mean ergodic theorem, Duke Math. J. 5 (1939), 635-646.
  • [6] N. Dunford and J. Schwartz, Linear Operators. Part I, Interscience, New York, 1958.
  • [7] M. I. Kadec and A. Pełczyński, Bases, lacunary sequences and complemented subspaces in the spaces $L_p$, Studia Math. 21 (1962), 161-176.
  • [8] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Springer, Berlin, 1977.
  • [9] A. Pełczyński, Projections in certain Banach spaces, Studia Math. 19 (1960), 209-228.
  • [10] A. Pełczyński, On strictly singular and strictly cosingular operators. II, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 37-41.
  • [11] H. Rosenthal, On relatively disjoint families of measures, with some applications to Banach space theory, Studia Math. 37 (1970), 13-36.
  • [12] E. Saab and P. Saab, On complemented copies of $c_0$ in injective tensor products, in: Contemp. Math. 52, Amer. Math. Soc., 1986, 131-135.
  • [13] I. Singer, Bases in Banach Spaces II, Springer, Berlin, 1981.
  • [14] A. Sobczyk, Projections of the space m on its subspace c, Bull. Amer. Math. Soc. 47 (1941), 78-106.
  • [15] W. Veech, Short proof of Sobczyk's theorem, Proc. Amer. Math. Soc. 28 (1971), 627-628.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-cmv80i2p235bwm
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