The Bourgain c 1-index of mixed Tsirelson space

  • Denny H. Leunga, Wee-Kee Tangb
  • Published 2003
Suppose that ðFnÞn1⁄40 is a sequence of regular families of finite subsets of N such that F0 contains all singletons, and ðynÞn1⁄41 is a nonincreasing null sequence in ð0; 1Þ: The mixed Tsirelson space TðF0; ðyn;FnÞn1⁄41Þ is the completion of c00 with respect to the implicitly defined norm jjxjj 1⁄4 max jjxjjF0 ; sup nAN sup yn Xk i1⁄41 jjEixjj ( ) ; where… (More)