On asymptotic structure, the szlenk index and UKK properties in Banach spaces

abstract

• 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.

authors

• Schlumprecht, Thomas

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

published in

• Positivity: an international journal devoted to the theory and applications of positivity in analysis  Journal

start page

• 173

end page

• 199

volume

• 3

issue

• 2