Indices, Convexity and Concavity of Calderón-lozanovskii Spaces
نویسندگان
چکیده
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.
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