Re: Riesz sequence = isomorphic embedding?

From: Robert Israel (israel_at_math.ubc.ca)
Date: 06/25/04 

Date: 25 Jun 2004 01:52:14 GMT

In article <f5547a6f.0406241727.462352ae@posting.google.com>,
Alex Gittens <bonobo@myrealbox.com> wrote:
>I'm stumped by this statement:

>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
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2