Department of Mathematics

ANALYSIS SEMINAR

"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.