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Comparison of Sums of Independent and Disjoint Functions in Symmetric Spaces

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Abstract

The sums of independent functions (random variables) in a symmetric space X on [0,1] are studied. We use the operator approach closely connected with the methods developed, primarily, by Braverman. Our main results concern the Orlicz exponential spaces exp(L_p), 1≤ p≤∞, and Lorentz spaces Λψ. As a corollary, we obtain results that supplement the well-known Johnson--Schechtman theorem stating that the condition L_p ⊂ X, p < ∞ implies the equivalence of the norms of sums of independent functions and their disjoint “copies.” In addition, a statement converse, in a certain sense, to this theorem is proved.

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Authors and Affiliations

  1. Samara State University, russia

    S. V. Astashkin

  2. Flinders University, Australia

    F. A. Sukochev

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  1. S. V. Astashkin
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  2. F. A. Sukochev
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Astashkin, S.V., Sukochev, F.A. Comparison of Sums of Independent and Disjoint Functions in Symmetric Spaces. Mathematical Notes 76, 449–454 (2004). https://doi.org/10.1023/B:MATN.0000043474.00734.ec

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  • DOI: https://doi.org/10.1023/B:MATN.0000043474.00734.ec

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