Abstract
We give simple necessary and sufficient conditions on Bessel sequences
{
f
i
}
and
{
g
i
}
and operators
L
1
,
L
2
on a Hilbert space
H
so that
{
L
1
f
i
+
L
2
g
i
}
is a frame for
H
. This allows us to construct a large number of new Hilbert space frames from existing frames.