2020/06/01 by Astashkin, Sergey V., Curbera, Guillermo P.
#46B09 #46B15 #46E30 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2006.00936
Let E be a rearrangement invariant (r.i.) function space on [0,1], and let ZE consist of all measurable functions f on (0,∞) such that f^*χ[0,1]∈ E and f^*χ[1,∞)∈ L2. We reveal close connections between properties of the generalized Rosenthal's space, corresponding to the space ZE, and the behaviour of independent symmetrically distributed random variables in E. The results obtained are applied to consider the problem of the existence of isomorphisms between r.i. spaces on [0,1] and (0,∞). Exploiting particular properties of disjoint sequences, we identify a rather wide new class of r.i. spaces on [0,1] ``close'' to L^∞, which fail to be isomorphic to r.i. spaces on (0,∞). In particular, this property is shared by the Lorentz spaces Λ2(log-α(e/u)), with 0