<s>
In	O
functional	B-Application
analysis	I-Application
and	O
related	O
areas	O
of	O
mathematics	O
,	O
distinguished	B-Algorithm
spaces	I-Algorithm
are	O
topological	B-Architecture
vector	I-Architecture
spaces	I-Architecture
(	O
TVSs	O
)	O
having	O
the	O
property	O
that	O
weak-*	O
bounded	O
subsets	O
of	O
their	O
biduals	O
(	O
that	O
is	O
,	O
the	O
strong	B-Algorithm
dual	I-Algorithm
space	I-Algorithm
of	O
their	O
strong	B-Algorithm
dual	I-Algorithm
space	I-Algorithm
)	O
are	O
contained	O
in	O
the	O
weak-*	O
closure	O
of	O
some	O
bounded	O
subset	O
of	O
the	O
bidual	O
.	O
</s>
<s>
Suppose	O
that	O
is	O
a	O
locally	B-Algorithm
convex	I-Algorithm
space	I-Algorithm
and	O
let	O
and	O
denote	O
the	O
strong	B-Algorithm
dual	I-Algorithm
of	O
(	O
that	O
is	O
,	O
the	O
continuous	O
dual	O
space	O
of	O
endowed	O
with	O
the	O
strong	B-Algorithm
dual	I-Algorithm
topology	I-Algorithm
)	O
.	O
</s>
<s>
A	O
Hausdorff	O
locally	B-Algorithm
convex	I-Algorithm
space	I-Algorithm
is	O
called	O
a	O
distinguished	B-Algorithm
space	I-Algorithm
if	O
it	O
satisfies	O
any	O
of	O
the	O
following	O
equivalent	O
conditions	O
:	O
</s>
<s>
The	O
strong	B-Algorithm
dual	I-Algorithm
of	O
is	O
a	O
barrelled	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
If	O
in	O
addition	O
is	O
a	O
metrizable	B-Algorithm
locally	B-Algorithm
convex	I-Algorithm
topological	I-Algorithm
vector	I-Algorithm
space	I-Algorithm
then	O
this	O
list	O
may	O
be	O
extended	O
to	O
include	O
:	O
</s>
<s>
(	O
Grothendieck	O
)	O
The	O
strong	B-Algorithm
dual	I-Algorithm
of	O
is	O
a	O
bornological	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
All	O
normed	O
spaces	O
and	O
semi-reflexive	O
spaces	O
are	O
distinguished	B-Algorithm
spaces	I-Algorithm
.	O
</s>
<s>
LF	B-Algorithm
spaces	I-Algorithm
are	O
distinguished	B-Algorithm
spaces	I-Algorithm
.	O
</s>
<s>
The	O
strong	B-Algorithm
dual	I-Algorithm
space	I-Algorithm
of	O
a	O
Fréchet	B-Algorithm
space	I-Algorithm
is	O
distinguished	O
if	O
and	O
only	O
if	O
is	O
quasibarrelled	B-Algorithm
.	O
</s>
<s>
Every	O
locally	B-Algorithm
convex	I-Algorithm
distinguished	B-Algorithm
space	I-Algorithm
is	O
an	O
H-space	O
.	O
</s>
<s>
The	O
strong	B-Algorithm
dual	I-Algorithm
of	O
a	O
distinguished	O
Banach	O
space	O
is	O
not	O
necessarily	O
separable	O
;	O
is	O
such	O
a	O
space	O
.	O
</s>
<s>
The	O
strong	B-Algorithm
dual	I-Algorithm
space	I-Algorithm
of	O
a	O
distinguished	O
Fréchet	B-Algorithm
space	I-Algorithm
is	O
not	O
necessarily	O
metrizable	B-Algorithm
.	O
</s>
<s>
There	O
exists	O
a	O
distinguished	O
semi-reflexive	O
non-reflexive	O
-quasibarrelled	O
Mackey	B-Algorithm
space	I-Algorithm
whose	O
strong	B-Algorithm
dual	I-Algorithm
is	O
a	O
non-reflexive	O
Banach	O
space	O
.	O
</s>
<s>
There	O
exist	O
H-spaces	O
that	O
are	O
not	O
distinguished	B-Algorithm
spaces	I-Algorithm
.	O
</s>
<s>
Fréchet	O
Montel	B-Algorithm
spaces	I-Algorithm
are	O
distinguished	B-Algorithm
spaces	I-Algorithm
.	O
</s>
