The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of
Studia Mathematica (1993)
- Volume: 104, Issue: 2, page 111-123
- ISSN: 0039-3223
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topDrewnowski, L., and Emmanuele, G.. "The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of $c_{0}$." Studia Mathematica 104.2 (1993): 111-123. <http://eudml.org/doc/215963>.
@article{Drewnowski1993,
abstract = {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.},
author = {Drewnowski, L., Emmanuele, G.},
journal = {Studia Mathematica},
keywords = {Banach space; isomorphic copy of $c_0$; spaces of vector measures; Bochner integrable functions; Radon-Nikodym property; uncomplemented subspace; Bochner space; Banach space of all -continuous vector measures; bounded variation; relatively compact range},
language = {eng},
number = {2},
pages = {111-123},
title = {The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of $c_\{0\}$},
url = {http://eudml.org/doc/215963},
volume = {104},
year = {1993},
}
TY - JOUR
AU - Drewnowski, L.
AU - Emmanuele, G.
TI - The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of $c_{0}$
JO - Studia Mathematica
PY - 1993
VL - 104
IS - 2
SP - 111
EP - 123
AB - 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.
LA - eng
KW - Banach space; isomorphic copy of $c_0$; spaces of vector measures; Bochner integrable functions; Radon-Nikodym property; uncomplemented subspace; Bochner space; Banach space of all -continuous vector measures; bounded variation; relatively compact range
UR - http://eudml.org/doc/215963
ER -
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Citations in EuDML Documents
top- Lech Drewnowski, Nonseparability of the quotient space cabv(∑,m;X)/L¹(m;X) for Banach spaces X without the Radon-Nikodym property
- María J. Rivera, On vector valued measure spaces of bounded -variation containing copies of
- Giovanni Emmanuele, Remarks on the complementability of spaces of Bochner integrable functions in spaces of vector measures
- Giovanni Emmanuele, On the position of the space of representable operators in the space of linear operators
- J. Bonet, Paweł Domański, M. Lindström, Cotype and complemented copies of in spaces of operators
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