On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables

DOI10.1007/BF02771562zbMath0213.19303OpenAlexW1969727526MaRDI QIDQ2544903

Haskell P. Rosenthal

Publication date: 1970

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02771562

Mathematics Subject Classification ID

Probability theory on algebraic and topological structures (60B99)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On totally incomparable Banach spaces
• On quasi-complemented subspaces of Banach spaces, with an appendix on compactness of operators from \(L^{p}(\mu)\) to \(L^{r}(\nu)\)
• Automorphisms in \(c_0\), \(\ell_1\) and \(m\)
• The \(L_ p\) spaces
• On bases and unconditional convergence of series in Banach spaces
• Projections in certain Banach spaces
• A Remarkable Series of Orthogonal Functions (I)
• Extension of compact operators
• Absolutely summing operators in $ℒ_{p}$-spaces and their applications
• On non-equivalent bases and conditional bases in Banach spaces
• Projections onto translation-invariant subspaces of 𝐿^{𝑝}(𝐺)