## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Friday, November 27, 2015 — 3:30 PM EST

**Niushan Ga, Southwest Jiaotong University **

“Unbounded Order Convergence in Banach lattices”

A net (xα) in a vector lattice X unbounded order converges to 0 if xα ∧ y →−o 0 in X for any uo

uo a.e.

In the case where X is a Banach function space, it can be shown that xn −→ 0 iff xn −−→ 0,

o a.e.

while xn →− 0 iff xn −−→ 0 and xn ≤ F for some F ∈ X and all n ≥ 1. The last condition

means that the sequence (xn) is order bounded, i.e. it is contained in an order interval [−F,F]. As this condition is generally difficult to satisfy, it suggests that unbounded order convergence is more useful than order convergence. In this talk, we discuss some fundamental properties of unbounded order convergence and also some applications of it. In particular, we use it to show that every Banach lattice has at most one (up to lattice isometries) order continuous predual.

MC 5403 **Please Note Room **

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1