Indices, convexity and concavity of Calderón-Lozanovskii spaces
- Autores: Anna Kaminska, L. Maligranda, L.-E. Persson
- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 92, Nº 1, 2003, págs. 141-160
- Idioma: inglés
- DOI: 10.7146/math.scand.a-14398
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Resumen
In this article we discuss lattice convexity and concavity of Calderón-Lozanovskii space $E_\varphi$, generated by a quasi-Banach space $E$ and an increasing Orlicz function $\varphi$. We give estimations of convexity and concavity indices of $E_\varphi$ in terms of Matuszewska-Orlicz indices of $\varphi$ as well as convexity and concavity indices of $E$. In the case when $E_\varphi$ is a rearrangement invariant space we also provide some estimations of its Boyd indices. As corollaries we obtain some necessary and sufficient conditions for normability of $E_\varphi$, and conditions on its nontrivial type and cotype in the case when $E_\varphi$ is a Banach space. We apply these results to Orlicz-Lorentz spaces receiving estimations, and in some cases the exact values of their convexity, concavity and Boyd indices.
