**Department of Mathematics**

**"****Unbounded Norm Topology in Banach Lattices****"**

**MOHAMMAD A. A.
MARABEH**

**(METU)**

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**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.

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**Date: ****Thursday, November 17,
2016**

**Time: ****13:40**

**Place: ****Mathematics Seminar,
SA-141**

Tea and cookies will be served before the
seminar.