Isomorphic Structure of Cesàro and Tandori Spaces

We investigate the isomorphic structure of the Cesàro spaces and their duals, the Tandori spaces. The main result states that the Cesàro function space Ces∞ and its sequence counterpart ces∞ are isomorphic. This is rather surprising since Ces∞ (like Talagrand’s example) has no natural lattice predual. We prove that ces∞ is not isomorphic to ℓ∞ nor is Ces∞ isomorphic to the Tandori space L1 with the norm ∥f∥L1 = ∥f∥L1, where f(t) = esssups≥tf(s). Our investigation also involves an examination of the Schur and Dunford–Pettis properties of Cesàro and Tandori spaces. In particular, using results of Bourgain we show that a wide class of Cesàro–Marcinkiewicz and Cesàro–Lorentz spaces have the latter property.Validerad;2019;Nivå 2;2019-06-18 (johcin)</p

Geometry of Cesaro function spaces

Geometric properties of CesA ro function spaces Ces (p) (I), where I = [0,a) or I = [0, 1], are investigated. In both cases, a description of their dual spaces for 1 &lt; p &lt; a is given. We find the type and the cotype of CesA ro spaces and present a complete characterization of the spaces l (q) that have isomorphic copies in Ces (p) [0, 1] (1 a (c) 1/2 p &lt; a).Validerad; 2011; 20110408 (andbra)</p