<s>
In	O
functional	B-Application
analysis	I-Application
,	O
a	O
Markushevich	B-Algorithm
basis	I-Algorithm
(	O
sometimes	O
M-basis	O
)	O
is	O
a	O
biorthogonal	B-Algorithm
system	I-Algorithm
that	O
is	O
both	O
complete	O
and	O
total	O
.	O
</s>
<s>
But	O
it	O
is	O
an	O
open	O
problem	O
whether	O
every	O
separable	O
Banach	O
space	O
admits	O
a	O
Markushevich	B-Algorithm
basis	I-Algorithm
with	O
for	O
all	O
.	O
</s>
<s>
An	O
example	O
of	O
a	O
Markushevich	B-Algorithm
basis	I-Algorithm
that	O
is	O
not	O
a	O
Schauder	O
basis	O
is	O
the	O
sequence	O
in	O
the	O
subspace	O
of	O
continuous	O
functions	O
from	O
to	O
the	O
complex	O
numbers	O
that	O
have	O
equal	O
values	O
on	O
the	O
boundary	O
,	O
under	O
the	O
supremum	O
norm	O
.	O
</s>
<s>
The	O
sequence	B-Algorithm
space	I-Algorithm
admits	O
no	O
Markushevich	B-Algorithm
basis	I-Algorithm
,	O
because	O
it	O
is	O
both	O
Grothendieck	O
and	O
irreflexive	O
.	O
</s>
<s>
complemented	O
in	O
a	O
space	O
admitting	O
a	O
Markushevich	B-Algorithm
basis	I-Algorithm
.	O
</s>
