Unconditional convergence of Gaussian random series in Banach spaces (Q2752974)
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scientific article; zbMATH DE number 1665908
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Unconditional convergence of Gaussian random series in Banach spaces |
scientific article; zbMATH DE number 1665908 |
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22 October 2001
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unconditional convergence
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Gaussian sequence
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0.9489885
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0.9236307
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0.91726446
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0.91548836
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0.91127366
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Unconditional convergence of Gaussian random series in Banach spaces (English)
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Let \(\xi_1,\xi_2,\ldots\) be centered Gaussian random variables with values in a Banach space \(X\) and with covariance operators \(R_k :X^*\to X\). The author gives sufficient conditions for the a.s.~unconditional convergence of \(\sum_{k=1}^\infty \xi_k\) in terms of properties of the \(R_k\)'s provided that \(X\) possesses an unconditional basis and does not contain \(l_\infty^n\)'s uniformly.
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