Indices, convexity and concavity of Calderón-Lozanovskii spaces - Kamińska, A.; Maligranda, L.; Persson, L. E. (Mathematica Scandinavica, 2003)
In this article we discuss lattice convexity and concavity of Calderón-Lozanovskii space $E_φ$, generated by a quasi-Banach space $E$ and an increasing Orlicz function $φ$. We give estimations of convexity and concavity indices of $E_φ$ in terms of Matuszewska-Orlicz indices of $φ$ as well as convexity and concavity indices of $E$. In the case when $E_φ$ 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 $E_φ$, and conditions on its nontrivial type and cotype in the case when $E_φ$ 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.