# Isomorphic and isometric copies of ${\ell}_{\infty}\left(\Gamma \right)$ 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 -

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