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

• Autorzy: Oscar Blasco
• Języki publikacji: EN

Abstrakty

EN

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 \(E=\ell_r\).

Słowa kluczowe

EN

multinorms; (p,q)-summing norm; Orlicz space; symmetric sequence space

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2016
• Tom: 56
• Numer: 1

Daty

wydano

2016

online

2016-10-13

Twórcy

autor

Oscar Blasco

Identyfikatory

DOI

10.14708/cm.v56i1.1105