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Block bases of the Haar system as complemented subspaces of $L_p$, $2<p<\infty$


Authors: Dvir Kleper and Gideon Schechtman
Journal: Proc. Amer. Math. Soc. 131 (2003), 433-439
MSC (2000): Primary 46E30
DOI: https://doi.org/10.1090/S0002-9939-02-06779-5
Published electronically: September 17, 2002
MathSciNet review: 1933334
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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 $L_p$.


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Additional 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
Email: gideon@wisdom.weizmann.ac.il

DOI: https://doi.org/10.1090/S0002-9939-02-06779-5
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 author’s M.Sc. thesis
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2002 American Mathematical Society

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