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

On the subspaces of L p ( p >2) spanned by sequences of independent random variables Abstract Let 2<p<∞. The Banach space spanned by a sequence of independent random variables inL p, each of mean zero, is shown to be isomorphic tol 2,l p,l 2⊕l p, or a new spaceX p , and the linear topological properties ofX p are investigated. It is proved thatX p is isomorphic to a complemented subspace ofL p and another uncomplemented subspace ofL p, whence there exists an uncomplemented subspace ofl p isomorphic tol p. It is also proved thatX p is not isomorphic to the previously knownℒ p spaces. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Israel Journal of Mathematics Springer Journals

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

Israel Journal of Mathematics , Volume 8 (3): 31 – Sep 1, 1970

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References (24)

Publisher
Springer Journals
Copyright
1970 Hebrew University
ISSN
0021-2172
eISSN
1565-8511
DOI
10.1007/BF02771562
Publisher site
See Article on Publisher Site

Abstract

Abstract Let 2<p<∞. The Banach space spanned by a sequence of independent random variables inL p, each of mean zero, is shown to be isomorphic tol 2,l p,l 2⊕l p, or a new spaceX p , and the linear topological properties ofX p are investigated. It is proved thatX p is isomorphic to a complemented subspace ofL p and another uncomplemented subspace ofL p, whence there exists an uncomplemented subspace ofl p isomorphic tol p. It is also proved thatX p is not isomorphic to the previously knownℒ p spaces.

Journal

Israel Journal of MathematicsSpringer Journals

Published: Sep 1, 1970

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