Asymptotically isometric and isometric copies of ${\ell }_1$ in some Banach function lattices

Anna Kamińska, and Mieczysław ~Mastyło. "Asymptotically isometric and isometric copies of $\ell _1$ in some Banach function lattices." Commentationes Mathematicae 53.2 (2013): null. <http://eudml.org/doc/292370>.

@article{AnnaKamińska2013,
abstract = {We identify the class of Caldern-Lozanovskii spaces that do not contain an asymptotically isometric copy of $\ell _1$, and consequently we obtain the corresponding characterizations in the classes of Orlicz-Lorentz and Orlicz spaces equipped with the Luxemburg norm. We also give a complete description of order continuous Orlicz-Lorentz spaces which contain (order) isometric copies of $\ell _1^\{(n)\}$ for each integer $n \ge 2$. As an application we provide necessary and sufficient conditions for order continuous Orlicz-Lorentz spaces to contain an (order) isometric copy of $\ell _1$. In particular we give criteria in Orlicz and Lorentz spaces for (order) isometric containment of $\ell _1^\{(n)\}$ and $\ell _1$. The results are applied to obtain the description of universal Orlicz-Lorentz spaces for all two-dimensional normed spaces.},
author = {Anna Kamińska, Mieczysław ~Mastyło},
journal = {Commentationes Mathematicae},
keywords = {Caldern-Lozanovskii spaces, Orlicz-Lorentz spaces, Orlicz spaces, Lorentz spaces, Marcinkiewicz spaces, isometric copies of $\ell _1^\{(n)\}$ and $\ell _1$, asymptotically isometric copies of $\ell _1$, fixed point property},
language = {eng},
number = {2},
pages = {null},
title = {Asymptotically isometric and isometric copies of $\ell _1$ in some Banach function lattices},
url = {http://eudml.org/doc/292370},
volume = {53},
year = {2013},
}

TY - JOUR
AU - Anna Kamińska
AU - Mieczysław ~Mastyło
TI - Asymptotically isometric and isometric copies of $\ell _1$ in some Banach function lattices
JO - Commentationes Mathematicae
PY - 2013
VL - 53
IS - 2
SP - null
AB - We identify the class of Caldern-Lozanovskii spaces that do not contain an asymptotically isometric copy of $\ell _1$, and consequently we obtain the corresponding characterizations in the classes of Orlicz-Lorentz and Orlicz spaces equipped with the Luxemburg norm. We also give a complete description of order continuous Orlicz-Lorentz spaces which contain (order) isometric copies of $\ell _1^{(n)}$ for each integer $n \ge 2$. As an application we provide necessary and sufficient conditions for order continuous Orlicz-Lorentz spaces to contain an (order) isometric copy of $\ell _1$. In particular we give criteria in Orlicz and Lorentz spaces for (order) isometric containment of $\ell _1^{(n)}$ and $\ell _1$. The results are applied to obtain the description of universal Orlicz-Lorentz spaces for all two-dimensional normed spaces.
LA - eng
KW - Caldern-Lozanovskii spaces, Orlicz-Lorentz spaces, Orlicz spaces, Lorentz spaces, Marcinkiewicz spaces, isometric copies of $\ell _1^{(n)}$ and $\ell _1$, asymptotically isometric copies of $\ell _1$, fixed point property
UR - http://eudml.org/doc/292370
ER -