Let
be the space of sequences
such that
, with inner product
and norm
.
I need to show that
is complete with respect to the inner product i.e. a Hilbert Space. I am assuming that
is complete.
I know that I need to show that every Cauchy sequence in H is convergent. I can see that this follows relatively easily from the definition of H.
So I have taken a sequence
but for this to be Cauchy
. But I can't see how to show that, given that the inner product on
has a
below it. Any help would be great. Thanks