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 **