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


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.


Banach Space Independent Random Variable Closed Subspace Usual Basis Unconditional Basis 
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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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