Nonseparability of the quotient space cabv(∑,m;X)/L¹(m;X) for Banach spaces X without the Radon-Nikodym property

• Autorzy: Lech Drewnowski
• Języki publikacji: EN

Abstrakty

EN

It is shown that if (S,∑,m) is an atomless finite measure space and X is a Banach space without the Radon-Nikodym property, then the quotient space cabv(∑,m;X)/L¹(m;X) is nonseparable.

Słowa kluczowe

EN

Banach space; spaces of vector measures; Bochner integrable functions; Radon-Nikodym property; nonseparable quotient space

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 104
• Numer: 2
• Strony: 125-132

Daty

wydano

1993

otrzymano

1991-05-14

poprawiono

1992-11-20

Twórcy

autor

Lech Drewnowski

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

Bibliografia

• [1] J. Bourgain, Dunford-Pettis operators on $L^1$ and the Radon-Nikodym property, Israel J. Math. 37 (1980), 34-47.
• [2] R. D. Bourgin, Geometric Aspects of Convex Sets with the Radon-Nikodým Property, Lecture Notes in Math. 993, Springer, Berlin 1983.
• [3] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, R.I., 1977.
• [4] L. Drewnowski, Another note on copies of $l_∞$ and $c_0$ in ca(Σ, X), and the equality ca(Σ, X) = cca(Σ, X), preprint, 1990.
• [5] L. Drewnowski and G. Emmanuele, The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of $c_0$, this volume, 111-123.
• [6] Z. Lipecki, Conditional and simultaneous extensions of group-valued quasi-measures, Glas. Mat. 19 (1984), 49-58.
• [7] R. D. Mauldin, Some effects of set-theoretical assumptions in measure theory, Adv. in Math. 27 (1978), 45-62.
• [8] A. Michalak, in preparation.