Block bases of the Haar system as complemented subspaces of $L_p$, $2<p<\infty$
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- by Dvir Kleper and Gideon Schechtman
- Proc. Amer. Math. Soc. 131 (2003), 433-439
- DOI: https://doi.org/10.1090/S0002-9939-02-06779-5
- Published electronically: September 17, 2002
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Abstract:
It is shown that the span of $\{a_ih_i\oplus b_i e_i \}^n_{i=1}$, where $\{h_i\}$ is the Haar system in $L_p$ and $\{e_i\}$ the canonical basis of $\ell _p$, is well isomorphic to a well complemented subspace of $L_p, \ 2<p<\infty$. As a consequence we get that there is a rearrangement of the (initial segments of the) Haar system in $L_p,\ 2<p<\infty$, any block basis of which is well isomorphic to a well complemented subspace of $L_p$.References
- D. L. Burkholder, Distribution function inequalities for martingales, Ann. Probability 1 (1973), 19β42. MR 365692, DOI 10.1214/aop/1176997023
- L. E. Dor and T. Starbird, Projections of $L_{p}$ onto subspaces spanned by independent random variables, Compositio Math. 39 (1979), no.Β 2, 141β175. MR 546965
- Paul F. X. MΓΌller and Gideon Schechtman, A remarkable rearrangement of the Haar system in $L_p$, Proc. Amer. Math. Soc. 125 (1997), no.Β 8, 2363β2371. MR 1389531, DOI 10.1090/S0002-9939-97-03860-4
- Haskell P. Rosenthal, On the subspaces of $L^{p}$ $(p>2)$ spanned by sequences of independent random variables, Israel J. Math. 8 (1970), 273β303. MR 271721, DOI 10.1007/BF02771562
- G. Schechtman, Complemented subspaces of $L_p$ and universal spaces. Ph.D. Thesis, Jerusalem, 1976 (in Hebrew).
- G. Schechtman, A remark on unconditional basic sequences in $L_{p}$ $(1<p<\infty )$, Israel J. Math. 19 (1974), 220β224. MR 511797, DOI 10.1007/BF02757716
- Elias M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory. , Annals of Mathematics Studies, No. 63, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1970. MR 0252961
Bibliographic Information
- Dvir Kleper
- Affiliation: Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel
- Email: dvir@wisdom.weizmann.ac.il
- Gideon Schechtman
- Affiliation: Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel
- MR Author ID: 155695
- Email: gideon@wisdom.weizmann.ac.il
- Received by editor(s): September 2, 2001
- Published electronically: September 17, 2002
- Additional Notes: The authors were supported in part by ISF. The results here form part of the first authorβs M.Sc. thesis
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 433-439
- MSC (2000): Primary 46E30
- DOI: https://doi.org/10.1090/S0002-9939-02-06779-5
- MathSciNet review: 1933334