Approximation of Subspaces of Symmetric Spaces Generated by Independent Functions

S. V. Astashkin

Matematičeskie zametki, Tome 96 (2014) no. 5, pp. 643-652.

Résumé

Let $E$ be a subspace of a symmetric space $X$ generated by $n$ independent identically distributed functions. It is proved that, under certain conditions on $X$, there exists a projection $P$, $\|P\|\le K$ ($K$ depending only on $X$) whose image contains $E$ and has dimension at most $Cn \ln(n + 1)$ ($C$ is independent of $n$ and $X$).

Détail

Keywords: uniformity function, independent functions, symmetric space, Orlicz space, Kruglov property.

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