On P. Levy's Stable Laws and Reflexive Subspaces of the Banach space L of Lebesgue summable functions on [0,1]

Details On P. Levy's Stable Laws and Reflexive Subspaces of the Banach space L of Lebesgue summable functions on [0,1] On P. Levy's Stable Laws and Reflexive Subspaces of the Banach space L of Lebesgue summable functions on [0,1]

2002-06-11

arxiv.org/abs/math/0206109v2

Mathematics

Functional Analysis

Latex2e; revised version

Scientific paper

To describe a set of functions, which forms a reflexive subspace B of the classical Banach space L a special function that characterizes their average integral growth is introduced. It is shown that this function essentially depends on the geometry of B. By the way, one question of la Vallee Poussin is answered. Also a short proof of the known result about the existence of an uncomplemented subspace isomorphic to the Hilbert space in every Lebesgue - Riesz space Lp (1

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