Advertisement

Israel Journal of Mathematics

, Volume 20, Issue 3–4, pp 216–227 | Cite as

A stability property of the unit vector basis ofl p

  • A. Szankowski
  • M. Zippin
Article

Abstract

Let {e n} be the unit vector basis ofl p, l<p<∞, and letx n=anen−bnen+1. Necessary and sufficient conditions are given for the operatorT:l p → span {x n} defined byTe i=xi to be invertible.

Keywords

Banach Space Quadratic Form Stability Property Stability Theorem Unit Vector Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C. Bessaga and A. Pełczyński,On bases and unconditional convergence of series in Banach spaces, Studia Math.17 (1958), 151–164.MATHMathSciNetGoogle Scholar
  2. 2.
    M. M. Day,Normed Linear Spaces. Springer-Verlag, 1962.Google Scholar
  3. 3.
    W. B. Johnson and M. Zippin,On subspaces of quotients ofG n)i p andG n)c0, Israel J. Math.13 (1972), 311–316.MathSciNetGoogle Scholar

Copyright information

© Hebrew University 1975

Authors and Affiliations

  • A. Szankowski
    • 1
    • 2
  • M. Zippin
    • 1
    • 2
  1. 1.The Hebrew University of JerusalemJerusalemIsrael
  2. 2.The Ohio State UniversityUSA

Personalised recommendations