Israel Journal of Mathematics

, Volume 15, Issue 2, pp 140–155 | Cite as

On symmetric basic sequences in Lorentz sequence spaces

  • Zvi Altshuler
  • P. G. Casazza
  • Bor-Luh Lin


We examine the symmetric basic sequences in some classes of Banach spaces with symmetric bases. We show that the Lorentz sequence spaced(a,p) has a unique symmetric basis and every infinite dimensional subspace ofd(a,p) contains a subspace isomorphic tol p. The symmetric basic sequences ind(a,p) are identified and a necessary and sufficient condition for a Lorents sequence space with exactly two nonequivalent symmetric basic sequences in given. We conclude by exhibiting an example of a Lorentz sequence space having a subspace with symmetric basis which is not isomorphic either to a Lorentz sequence space or to anl p-space.


Banach Space Sequence Space Basic Sequence Nonnegative Number Unit Vector Basis 
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Copyright information

© The Weizmann Science Press of Israel 1973

Authors and Affiliations

  • Zvi Altshuler
    • 1
    • 2
    • 3
  • P. G. Casazza
    • 1
    • 2
    • 3
  • Bor-Luh Lin
    • 1
    • 2
    • 3
  1. 1.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael
  2. 2.Department of MathematicsThe University of AlabamaHuntsvilleU.S.A.
  3. 3.Department of MathematicsThe University of IowaIowa CityU.S.A.

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