Fragmentability and σ-fragmentability

• Autorzy: J. E. Jayne , I. Namioka , C. A. Rogers
• Języki publikacji: EN

Abstrakty

EN

Recent work has studied the fragmentability and σ-fragmentability properties of Banach spaces. Here examples are given that justify the definitions that have been used. The fragmentability and σ-fragmentability properties of the spaces $ℓ^∞$ and $ℓ_c^∞({Γ})$, with Γ uncountable, are determined.

Kategorie tematyczne

• 46B26: Nonseparable Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1993
• Tom: 143
• Numer: 3
• Strony: 207-220

Daty

wydano

1993

otrzymano

1992-09-02

poprawiono

1993-05-14

Twórcy

autor

J. E. Jayne

• Department of Mathematics, University College London, Gower Street, London WC1E 6BT, U.K.

autor

I. Namioka

• Department of Mathematics, GN-50, University of Washington, Seattle, Washington 98195, U.S.A.

autor

C. A. Rogers

• Department of Mathematics, University College London, Gower Street, London WC1E 6BT, U.K.

Bibliografia

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• [4] R. Haydon and C. A. Rogers, A locally uniformly convex renorming for certain C(K), Mathematika 37 (1990), 1-8.
• [5] J. E. Jayne, I. Namioka and C. A. Rogers, Norm fragmented weak compact sets, Collect. Math. 41 (1990), 133-163.
• [6] J. E. Jayne, I. Namioka and C. A. Rogers, σ-Fragmented Banach spaces, Mathematika 39 (1992), 161-188 and 197-215.
• [7] J. E. Jayne, I. Namioka and C. A. Rogers, Topological properties of Banach spaces, Proc. London Math. Soc. (3) 66 (1993), 651-672.
• [8] J. E. Jayne, I. Namioka and C. A. Rogers, σ-Fragmented Banach spaces, II, preprint.
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• [16] Z. Semadeni, Banach Spaces of Continuous Functions, Vol. 1, PWN, Warszawa, 1971.