Talk:Closed operator
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 | The contents of the Closed operator page were merged into Unbounded operator on 2 Nov 2012 and it now redirects there. For the contribution history and old versions of the merged article please see its history. |
Equivalent Definition?[edit]
A function is closed in the topological sense if it sends closed sets to closed sets. Is the notion of closed operator in the functional analysis sense equivalent to the notion of closed in the topological sense?
72.67.37.221 (talk) 23:53, 2 January 2012 (UTC)
- Probably not. Rather, a closed operator is a special case of a function whose graph is closed. Boris Tsirelson (talk) 09:57, 3 January 2012 (UTC)
Unbounded operator[edit]
Note: Unbounded operator redirects here but this page provides no information on that topic yet. —Ben FrantzDale 00:20, 15 December 2006 (UTC)
This article gives the wrong suggestion that a closed operator needs to be defined on a linear subspace of some space B with values in the same space B. Actually the domain and range of a closed operator can be contained in different spaces.˜˜˜˜
Agreed. I've changed it accordingly. (And Unbounded operator doesn't redirect here any longer) Simplifix (talk) 12:08, 2 February 2010 (UTC)
- Unfortunately, the article is now inconsistent. The basic property number 2 makes no sense in the case of two spaces. And the phrase "one can define the spectrum and (with certain assumptions) functional calculus for such operators" in the lead became false.Boris Tsirelson (talk) 15:54, 2 February 2010 (UTC)
- Still inconsistent! Boris Tsirelson (talk) 09:58, 3 January 2012 (UTC)