<s>
In	O
mathematics	O
,	O
an	O
Orlicz	B-Algorithm
sequence	I-Algorithm
space	I-Algorithm
is	O
any	O
of	O
certain	O
class	O
of	O
linear	O
spaces	O
of	O
scalar-valued	O
sequences	B-Algorithm
,	O
endowed	O
with	O
a	O
special	O
norm	O
,	O
specified	O
below	O
,	O
under	O
which	O
it	O
forms	O
a	O
Banach	O
space	O
.	O
</s>
<s>
Orlicz	B-Algorithm
sequence	I-Algorithm
spaces	I-Algorithm
generalize	O
the	O
spaces	O
,	O
and	O
as	O
such	O
play	O
an	O
important	O
role	O
in	O
functional	B-Application
analysis	I-Application
.	O
</s>
<s>
We	O
then	O
define	O
the	O
Orlicz	B-Algorithm
sequence	I-Algorithm
space	I-Algorithm
with	O
respect	O
to	O
,	O
denoted	O
,	O
as	O
the	O
linear	O
space	O
of	O
all	O
such	O
that	O
for	O
some	O
,	O
endowed	O
with	O
the	O
norm	O
.	O
</s>
<s>
We	O
denote	O
by	O
the	O
subspace	O
of	O
scalar	O
sequences	B-Algorithm
such	O
that	O
for	O
all	O
.	O
</s>
<s>
(	O
See	O
the	O
example	O
below	O
of	O
an	O
Orlicz	B-Algorithm
sequence	I-Algorithm
space	I-Algorithm
with	O
two	O
nonequivalent	O
symmetric	O
bases	O
.	O
)	O
</s>
<s>
Let	O
be	O
an	O
infinite-dimensional	O
closed	O
subspace	O
of	O
a	O
separable	O
Orlicz	B-Algorithm
sequence	I-Algorithm
space	I-Algorithm
.	O
</s>
<s>
Then	O
has	O
a	O
subspace	O
isomorphic	O
to	O
some	O
Orlicz	B-Algorithm
sequence	I-Algorithm
space	I-Algorithm
for	O
some	O
Orlicz	O
function	O
satisfying	O
the	O
Δ2	O
condition	O
at	O
zero	O
.	O
</s>
<s>
Every	O
separable	O
Orlicz	B-Algorithm
sequence	I-Algorithm
space	I-Algorithm
contains	O
a	O
subspace	O
isomorphic	O
to	O
for	O
some	O
.	O
</s>
<s>
Every	O
infinite-dimensional	O
closed	O
subspace	O
of	O
a	O
separable	O
Orlicz	B-Algorithm
sequence	I-Algorithm
space	I-Algorithm
contains	O
a	O
further	O
subspace	O
isomorphic	O
to	O
for	O
some	O
.	O
</s>
<s>
There	O
exists	O
a	O
separable	O
and	O
reflexive	O
Orlicz	B-Algorithm
sequence	I-Algorithm
space	I-Algorithm
which	O
fails	O
to	O
contain	O
a	O
complemented	O
copy	O
of	O
for	O
any	O
.	O
</s>
<s>
If	O
is	O
an	O
Orlicz	B-Algorithm
sequence	I-Algorithm
space	I-Algorithm
satisfying	O
(	O
i.e.	O
,	O
the	O
two-sided	O
limit	O
exists	O
)	O
then	O
the	O
following	O
are	O
all	O
true	O
.	O
</s>
