Department of Mathematics
"Unbounded Norm Topology in Banach Lattices"
MOHAMMAD A. A.
MARABEH
(METU)
Abstract: A net in a Banach lattice is said to be unbounded
norm convergent or un-convergent to if for all . In this talk, we investigate un-topology,
i.e., the topology that corresponds to un-convergence. We will see that un-
topology agrees with the norm topology iff has a strong unit.
Un-topology is metrizable iff
has a quasi-interior
point. Suppose that is order continuous,
then un-topology is locally convex iff is atomic. An order
continuous Banach lattice is a KB-space iff its closed unit ball is un-complete. For a Banach lattice, is un-compact iff is an atomic KB-space.
Date: Thursday, November 17,
2016
Time: 13:40
Place: Mathematics Seminar, SA-141
Tea and cookies will be served before the
seminar.