Indices, convexity and concavity of Calderón-Lozanovskii spaces
In this article we discuss lattice convexity and concavity of Calderón-Lozanovskii space Eφ, generated by a quasi-Banach space E and an increasing Orlicz function φ. We give estimations of convexity and concavity indices of Eφ in terms of Matuszewska-Orlicz indices of φ as well as convexity and concavity indices of E. In the case when Eφ 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 Eφ, and conditions on its nontrivial type and cotype in the case when Eφ 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.
Kamińska, A., Maligranda, L., & Persson, L. (2003). Indices, convexity and concavity of Calderón-Lozanovskii spaces. Mathematica Scandinavica, 92 (1), 141-160. https://doi.org/10.7146/math.scand.a-14398