Uniform Kadec-Klee Property in Banach lattices

Details Uniform Kadec-Klee Property in Banach lattices Uniform Kadec-Klee Property in Banach lattices

1994-06-06

arxiv.org/abs/math/9406209v1

Mathematics

Functional Analysis

Scientific paper

We prove that a Banach lattice $X$ which does not contain the
$l^n_{\infty}$-uniformly has an equivalent norm which is uniformly Kadec-Klee
for a natural topology $\tau$ on $X$. In case the Banach lattice is purely
atomic, the topology $\tau$ is the coordinatewise convergence topology.

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