The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of $c_{0}$

• Autorzy: L. Drewnowski , G. Emmanuele
• Języki publikacji: EN

Abstrakty

EN

Let (S, ∑, m) be any atomless finite measure space, and X any Banach space containing a copy of $c_0$. Then the Bochner space $L^1(m;X)$ is uncomplemented in ccabv(∑,m;X), the Banach space of all m-continuous vector measures that are of bounded variation and have a relatively compact range; and ccabv(∑,m;X) is uncomplemented in cabv(∑,m;X). It is conjectured that this should generalize to all Banach spaces X without the Radon-Nikodym property.

Słowa kluczowe

EN

Banach space; isomorphic copy of $c_0$; spaces of vector measures; Bochner integrable functions; Radon-Nikodym property; uncomplemented subspace

Kategorie tematyczne

• 46B22: Radon-Nikod{\'y}m, Kre{\u\i}n-Milman and related properties
• 46B20: Geometry and structure of normed linear spaces
• 46B45: Banach sequence spaces
• 46B03: Isomorphic theory (including renorming) of Banach spaces
• 46E27: Spaces of measures
• 46B25: Classical Banach spaces in the general theory
• 46G10: Vector-valued measures and integration

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 104
• Numer: 2
• Strony: 111-123

Daty

wydano

1993

otrzymano

1991-05-14

poprawiono

1992-11-20

Twórcy

autor

L. Drewnowski

• Institute of Mathematics, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland,

autor

G. Emmanuele

• Department of Mathematics, University of Catania, Viale A. Doria 6, 95125 Catania, Italy,

Bibliografia

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