2
$\begingroup$

Hi Everyone,

I was recently reading Reed & Simon's functional analysis textbook (the first volume), and it mentions casually on page 294 that weak graph limits of a sequence of symmetric operators are not necessarily closed. However no example (or a reference to one) is given. I've tried to construct one but nothing simple seems to work.

Does anyone know of some such example or at least of a reference where one is discussed?

Thanks

Improve this question
$\endgroup$
1
  • 3
    $\begingroup$ In my copy (the 1972 edition) it says "It is an open question whether weak graph limits are necessarily closed if each $A_n$ is symmetric". I see in Google Books on-line preview (which is of the 1980 edition) "It is not true that weak graph limits are necessarily closed if each $A_n$ is symmetric". So apparently an example was found (or was brought to the authors' attention) between 1972 and 1980. $\endgroup$
    – Robert Israel
    Commented Aug 29, 2012 at 8:19

0

Reset to default

You must log in to answer this question.