On asymptotic structure, the szlenk index and UKK properties in Banach spaces Academic Article uri icon


  • Let B be a separable Banach space and let X = B* be separable. We prove that if B has finite Szlenk index (for all > 0) then B can be renormed to have the weak* uniform Kadec-Klee property. Thus if > 0 there exists () > 0 so that if (xn) is a sequence in the ball of X converging * to x so that lim infn ||xn - x|| then ||x|| 1 - (). In addition we show that the norm can be chosen so that () cp for some p < and c > 0. 1999 Kluwer Academic Publishers.

published proceedings

  • Positivity

author list (cited authors)

  • Knaust, H., Odell, E., & Schlumprecht, T.

complete list of authors

  • Knaust, H||Odell, E||Schlumprecht, T

publication date

  • December 1999