On inclusion relations between Lorentz sequence spaces and inequalities of Lewis type
- Autores: Nicolae Tita
- Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 36, Fasc. 1, 1985, págs. 113-118
- Idioma: inglés
- Títulos paralelos:
- Sobre relaciones de inclusión entre espacios de sucesiones de Lorentz y desigualdades de tipo Lewis
- Enlaces
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Resumen
Are well known the Lorentz sequence spaces $\ell_{p,q}$ and the relations $\ell_{p,q}\subset\ell_{p_1,q}$ if $1\leqslant p ?p_1\leqslant\infty$ and $\ell_{p,q}\subset\ell_{p,q_1}$ if $1\leqslant p\leqslant\infty, 1\leqslant q ? q_1 ? \infty$ [4],[5],[1]. In this paper a generalization of these spaces is considered using the symmetric norming functions of $\mathfrak{R}$. Schatten [2], [8], [9] and some inclusion relations are presented. In the second part of the paper theses inclusion relations are utilised to establish inequalities of Lewis type [1], [7] for some operator ideals generated by an additive $s$-function ($s-$number) [5], [6], [11].
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