Functional Analysis and Its Applications

, Volume 47, Issue 2, pp 148–151 | Cite as

On complementability of subspaces in symmetric spaces with the Kruglov property

  • S. V. Astashkin
Brief Communications


We show that, for a broad class of symmetric spaces on [0, 1], the complementability of the subspace generated by independent functions f k (k = 1, 2,…) is equivalent to the complementability of the subspace generated by the disjoint translates \(\bar f_k (t) = f_k (t - k + 1)\chi _{[k - 1,k]} (t)\) of these functions in some symmetric space Z X 2 on the semiaxis [0,∞). Moreover, if Σ k=1 m(supp f k ) ⩽ 1, then Z X 2 can be replaced by X itself. This result is new even in the case of L p -spaces. A series of consequences is obtained; in particular, for the class of symmetric spaces, a result similar to a well-known theorem of Dor and Starbird on the complementability in L p [0, 1] (1 ⩽ p < ) of the subspace [f k ] generated by independent functions provided that it is isomorphic to the space l p is obtained.

Key words

complemented subspace independent functions Rademacher functions symmetric space Kruglov property Boyd indices lower p-estimate 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Samara State UniversitySamaraRussia

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