DOI: 10.68381/jca21035 ISSN: 0944-6532
Order Asymptotically Isometric Copies of c
o
in the Subspaces of Order Continuous Elements in Orlicz Spaces
Yunan Cui, Henryk Hudzik, Grzegorz Lewicki
Necessary and sufficient conditions in order that the subspace of order continuous elements of Orlicz sequence space contain an order asymptotically isometric copy of
c_0
c
0
are given for both, the Luxemburg and the Amemiya-Orlicz norm. In case of a non-atomic, complete and
\sigma-
σ
−
finite measure space
(T,\Sigma,\mu)
(
T
,
Σ
,
μ
)
and the Luxemburg norm (the Amemiya-Orlicz norm) such criteria are obtained under the additional assumption that the space
L^\Phi(T,\Sigma,\mu)
L
Φ
(
T
,
Σ
,
μ
)
is a dual space (resp. the space
L^\Phi_A(T,\Sigma,\mu)
L
A
Φ
(
T
,
Σ
,
μ
)
is a dual and non-square space). In both cases, the Luxemburg and the Amemiya-Orlicz norm the criteria are given under the necessary assumption that the spaces
E^\Phi(T,\Sigma,\mu)
E
Φ
(
T
,
Σ
,
μ
)
and
E^\Phi_A(T,\Sigma,\mu)
E
A
Φ
(
T
,
Σ
,
μ
)
are non-trivial. The asymptotically isometric copies of
c_0
c
0
that are built in our theorems are order copies.