Geodesic
Summing multi-norms defined by Orlicz spaces and symmetric sequence space
Commentationes Mathematicae, Tome 56 (2016) no. 1, p. 145−168.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

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 \(\|(\delta_1,\cdots,\delta_n)\|_n^{(X_1,X_2)}\) 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 \(E=\ell_r\).
DOI : 10.14708/cm.v56i1.1105
Classification : Primary 46B45;46E30 Secondary 46B20, 46B70
Mots-clés : multinorms, (p,q)-summing norm, Orlicz space, symmetric sequence space 
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Oscar Blasco. Summing multi-norms defined by Orlicz spaces and symmetric sequence space. Commentationes Mathematicae, Tome 56 (2016) no. 1, p.  145−168. doi : 10.14708/cm.v56i1.1105. http://geodesic.mathdoc.fr/articles/10.14708/cm.v56i1.1105/

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