Re: Riesz sequence = isomorphic embedding?

From: Alex Gittens (bonobo_at_myrealbox.com)
Date: 06/25/04 

Date: 25 Jun 2004 08:13:48 -0700

> >A Riesz sequence in H (a Hilbert space) is the image of the unit
> >vector basis in l_2 (the space of square summable sequences) under an
> >isomorphic embedding.
>
> >What is an isomorphic embedding? (there is no mention of either of
> >those terms up to the point where the statement is made).
>
> It's a linear map, in this case from l_2 into H, which is 1-1 and
> has closed range, but not necessarily onto. Thus it has a continuous
> inverse defined on that range.
>
> Robert Israel israel@math.ubc.ca

Ok, so is this the idea:
'embedding' refers to injectivity,
'isomorphic' refers to preserving the vector space structure
(linearity in addition and scalar multiplication)?

Is the idea of closed range implied by 'embedding'?