Resumen de On inclusion relations between Lorentz sequence spaces and inequalities of Lewis type

Nicolae Tita

• 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].