Isomorphic and isometric copies of in duals of Banach spaces and Banach lattices
Commentationes Mathematicae Universitatis Carolinae (2006)
- Volume: 47, Issue: 3, page 467-471
- ISSN: 0010-2628
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topWójtowicz, Marek. "Isomorphic and isometric copies of $\ell _\infty (\Gamma )$ in duals of Banach spaces and Banach lattices." Commentationes Mathematicae Universitatis Carolinae 47.3 (2006): 467-471. <http://eudml.org/doc/249837>.
@article{Wójtowicz2006,
abstract = {Let $X$ and $E$ be a Banach space and a real Banach lattice, respectively, and let $\Gamma $ denote an infinite set. We give concise proofs of the following results: (1) The dual space $X^*$ contains an isometric copy of $c_0$ iff $X^*$ contains an isometric copy of $\ell _\infty $, and (2) $E^*$ contains a lattice-isometric copy of $c_0(\Gamma )$ iff $E^*$ contains a lattice-isometric copy of $\ell _\infty (\Gamma )$.},
author = {Wójtowicz, Marek},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {isometry; embedding of $\ell _\infty $; dual space; Banach lattice; isometry; embedding of ; dual space},
language = {eng},
number = {3},
pages = {467-471},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Isomorphic and isometric copies of $\ell _\infty (\Gamma )$ in duals of Banach spaces and Banach lattices},
url = {http://eudml.org/doc/249837},
volume = {47},
year = {2006},
}
TY - JOUR
AU - Wójtowicz, Marek
TI - Isomorphic and isometric copies of $\ell _\infty (\Gamma )$ in duals of Banach spaces and Banach lattices
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 3
SP - 467
EP - 471
AB - Let $X$ and $E$ be a Banach space and a real Banach lattice, respectively, and let $\Gamma $ denote an infinite set. We give concise proofs of the following results: (1) The dual space $X^*$ contains an isometric copy of $c_0$ iff $X^*$ contains an isometric copy of $\ell _\infty $, and (2) $E^*$ contains a lattice-isometric copy of $c_0(\Gamma )$ iff $E^*$ contains a lattice-isometric copy of $\ell _\infty (\Gamma )$.
LA - eng
KW - isometry; embedding of $\ell _\infty $; dual space; Banach lattice; isometry; embedding of ; dual space
UR - http://eudml.org/doc/249837
ER -
References
top- Abramovich Y.A., Wickstead A.W., When each continuous operator is regular. II, Indag. Math., N.S. 8 (1997), 281-294. (1997) Zbl0908.47031MR1622216
- Aliprantis C.D., Burkinshaw O., Positive Operators, Academic Press, New York, 1985. Zbl1098.47001MR0809372
- Bessaga C., Pełczyński A., On basis and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151-164. (1958) MR0115069
- Dowling P.N., Isometric copies of and in duals of Banach spaces, J. Math. Anal. Appl. 244 (2000), 223-227. (2000) Zbl0955.46011MR1746799
- Lindenstrauss J., Tzafriri L., Classical Banach Spaces. I, Springer, Berlin, 1977. Zbl0362.46013MR0500056
- Meyer-Nieberg P., Banach Lattices, Springer, Berlin, 1991. Zbl0743.46015MR1128093
- Rosenthal H.P., On injective Banach spaces and the spaces for finite measures , Acta Math. 124 (1974), 205-247. (1974) MR0257721
- Rosenthal H.P., On relatively disjoint families of measures, with some applications to Banach space theory, Studia Math. 37 (1970), 13-36. (1970) Zbl0227.46027MR0270122
- Wójtowicz M., The Sobczyk property and copies of in locally convex-solid Riesz spaces, Arch. Math. 75 (2000), 376-379. (2000) MR1785446
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