<s>
In	O
operator	O
theory	O
,	O
a	O
multiplication	B-Algorithm
operator	I-Algorithm
is	O
an	O
operator	O
defined	O
on	O
some	O
vector	B-Algorithm
space	I-Algorithm
of	I-Algorithm
functions	I-Algorithm
and	O
whose	O
value	O
at	O
a	O
function	O
is	O
given	O
by	O
multiplication	O
by	O
a	O
fixed	O
function	O
.	O
</s>
<s>
for	O
all	O
in	O
the	O
domain	B-Algorithm
of	O
,	O
and	O
all	O
in	O
the	O
domain	B-Algorithm
of	O
(	O
which	O
is	O
the	O
same	O
as	O
the	O
domain	B-Algorithm
of	O
)	O
.	O
</s>
<s>
This	O
type	O
of	O
operator	O
is	O
often	O
contrasted	O
with	O
composition	B-Algorithm
operators	I-Algorithm
.	O
</s>
<s>
Multiplication	B-Algorithm
operators	I-Algorithm
generalize	O
the	O
notion	O
of	O
operator	O
given	O
by	O
a	O
diagonal	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
More	O
precisely	O
,	O
one	O
of	O
the	O
results	O
of	O
operator	O
theory	O
is	O
a	O
spectral	O
theorem	O
that	O
states	O
that	O
every	O
self-adjoint	O
operator	O
on	O
a	O
Hilbert	O
space	O
is	O
unitarily	O
equivalent	O
to	O
a	O
multiplication	B-Algorithm
operator	I-Algorithm
on	O
an	O
L2	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
Consider	O
the	O
Hilbert	O
space	O
of	O
complex-valued	O
square	B-Algorithm
integrable	I-Algorithm
functions	I-Algorithm
on	O
the	O
interval	O
.	O
</s>
<s>
This	O
will	O
be	O
a	O
self-adjoint	O
bounded	O
linear	O
operator	O
,	O
with	O
domain	B-Algorithm
all	O
of	O
and	O
with	O
norm	O
.	O
</s>
<s>
Its	O
spectrum	O
will	O
be	O
the	O
interval	O
(	O
the	O
range	B-Algorithm
of	O
the	O
function	O
defined	O
on	O
)	O
.	O
</s>
<s>
which	O
is	O
another	O
multiplication	B-Algorithm
operator	I-Algorithm
.	O
</s>
<s>
This	O
can	O
be	O
easily	O
generalized	O
to	O
characterizing	O
the	O
norm	O
and	O
spectrum	O
of	O
a	O
multiplication	B-Algorithm
operator	I-Algorithm
on	O
any	O
Lp	O
space	O
.	O
</s>
