A Problem on Spreading Models Academic Article uri icon

abstract

  • It is proved that if a Banach spaceXhas a basis (en) satisfying every spreading model of a normalized block basis of (en) is 1-equivalent to the unit vector basis of 1 (respectively,c0) thenXcontains 1(respectively,c0). Furthermore, Tsirelson's spaceTis shown to have the property that every infinite dimensional subspace contains a sequence having spreading model 1-equivalent to the unit vector basis of 1. An equivalent norm is constructed onTso that s1+s2<2 whenever (sn) is a spreading model of a normalized basic sequence inT. 1998 Academic Press.

published proceedings

  • Journal of Functional Analysis

author list (cited authors)

  • Odell, E., & Schlumprecht, T. h.

citation count

  • 10

complete list of authors

  • Odell, E||Schlumprecht, Th

publication date

  • March 1998