Summing multi-norms defined by Orlicz spaces and symmetric sequence space

Oscar Blasco. "Summing multi-norms defined by Orlicz spaces and symmetric sequence space." Commentationes Mathematicae 56.1 (2016): null. <http://eudml.org/doc/292473>.

@article{OscarBlasco2016,
abstract = {We develop the notion of the $(X_1,X_2)$-summing power-norm based on a Banach space $E$, where $X_1$ and $X_2$ are symmetric sequence spaces. We study the particular case when $X_1$ and $X_2$ are Orlicz spaces $\ell _\Phi $ and $\ell _\Psi $ respectively and analyze under which conditions the $(\Phi , \Psi )$-summing power-norm becomes a multinorm. In the case when $E$ is also a symmetric sequence space $L$, we compute the precise value of $\Vert (\delta _1,\cdots ,\delta _n)\Vert _n^\{(X_1,X_2)\}$ where $(\delta _k)$ stands for the canonical basis of $L$, extending known results for the $(p,q)$-summing power-norm based on the space $\ell _r$ which corresponds to $X_1=\ell _p$, $X_2=\ell _q$, and $E=\ell _r$.},
author = {Oscar Blasco},
journal = {Commentationes Mathematicae},
keywords = {multinorms; (p,q)-summing norm; Orlicz space; symmetric sequence space},
language = {eng},
number = {1},
pages = {null},
title = {Summing multi-norms defined by Orlicz spaces and symmetric sequence space},
url = {http://eudml.org/doc/292473},
volume = {56},
year = {2016},
}

TY - JOUR
AU - Oscar Blasco
TI - Summing multi-norms defined by Orlicz spaces and symmetric sequence space
JO - Commentationes Mathematicae
PY - 2016
VL - 56
IS - 1
SP - null
AB - We develop the notion of the $(X_1,X_2)$-summing power-norm based on a Banach space $E$, where $X_1$ and $X_2$ are symmetric sequence spaces. We study the particular case when $X_1$ and $X_2$ are Orlicz spaces $\ell _\Phi $ and $\ell _\Psi $ respectively and analyze under which conditions the $(\Phi , \Psi )$-summing power-norm becomes a multinorm. In the case when $E$ is also a symmetric sequence space $L$, we compute the precise value of $\Vert (\delta _1,\cdots ,\delta _n)\Vert _n^{(X_1,X_2)}$ where $(\delta _k)$ stands for the canonical basis of $L$, extending known results for the $(p,q)$-summing power-norm based on the space $\ell _r$ which corresponds to $X_1=\ell _p$, $X_2=\ell _q$, and $E=\ell _r$.
LA - eng
KW - multinorms; (p,q)-summing norm; Orlicz space; symmetric sequence space
UR - http://eudml.org/doc/292473
ER -