- Tytuł:
- Summing multi-norms defined by Orlicz spaces and symmetric sequence space
- Autorzy:
- Blasco, Oscar
- Powiązania:
- https://bibliotekanauki.pl/articles/745023.pdf
- Data publikacji:
- 2016
- Wydawca:
- Polskie Towarzystwo Matematyczne
- Tematy:
-
multinorms
(p,q)-summing norm
Orlicz space
symmetric sequence space - Opis:
- 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 \(E=\ell_r\).
- Źródło:
-
Commentationes Mathematicae; 2016, 56, 1
0373-8299 - Pojawia się w:
- Commentationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł