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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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 PDF
Proc. Amer. Math. Soc. 131 (2003), 433-439 Request permission

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
  • 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 author’s 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