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Israel Journal of Mathematics

, Volume 8, Issue 3, pp 273–303 | Cite as

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

  • Haskell P. Rosenthal
Article

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 2l 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 known p spaces.

Keywords

Banach Space Independent Random Variable Closed Subspace Usual Basis Unconditional Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University 1970

Authors and Affiliations

  • Haskell P. Rosenthal
    • 1
  1. 1.University of CaliforniaBerkeley

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