A remark on unconditional basic sequences inL _p (1<p<∞)

Abstract

We prove that every separable ℒ _p space (1<p<∞), with an unconditional basis is isomorphic to a complemented subspace ofL _p which is spanned by a block basis of the Haar system.

Similar content being viewed by others

On unconditional basis property in the space H ¹(R) of a system of Franklin functions with vanishing means

Article 01 November 2016

The Hahn sequence space generated by the Cesàro mean of order m

Article 02 November 2023

On certain subspaces of \({\ell _p}\) for \({0 and their applications to conditional quasi-greedy bases in p-Banach spaces

Article 01 October 2020

Author information

Authors and Affiliations

1. Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

   G. Schechtman

Authors

1. G. Schechtman
   View author publications

   You can also search for this author in PubMed Google Scholar

Additional information

This is part of the author's Ph.D. thesis written at the Hebrew University of Jerusalem under the supervision of Professor J. Lindenstrauss.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schechtman, G. A remark on unconditional basic sequences inL _p (1<p<∞). Israel J. Math. 19, 220–224 (1974). https://doi.org/10.1007/BF02757716

Download citation

• Received: 01 April 1974

• Issue Date: September 1974

• DOI: https://doi.org/10.1007/BF02757716

Keywords

• Banach Space
• Block Basis
• Basic Sequence
• Trigonometric Series
• Unconditional Basis