Talk:Functional analysis
Merge?
The following discussion relates to a now abandoned proposal to merge this article with calculus of variations.
Really, no way should this page be merged with calculus of variations. Phys, my man, these subjects diverged nearly a century ago. Charles Matthews 07:56, 5 Sep 2003 (UTC)
- I'm inclined to agree here. Dysprosia 08:01, 5 Sep 2003 (UTC)
Additional remarks. I'm sure much of this is wrong, and much of the rest is POV. Some infinite-dimensional spaces can be shown to have a basis without AC, surely. Hahn-Banach can be side-stepped in separable spaces. And the advice is not necessarily good. Is any of this really important to keep?
- I fixed the remark saying that Hahn-Banach requires AC. Hahn-Banach can only be side-stepped in separable spaces if one allows DC. The comment about infinite-dimensional spaces is correct, I would think, because almost all spaces actually considered in functional analysis can not be shown to have a basis without essentially using AC for some cardinal. However, there is no reason why it should say Zorn's lemma instead of the axiom of choice, and the point is largely irrelevant for functional analysis, as there are very few cases where one actually needs a Hamel basis for a particular infinite-dimensional Banach space.
Charles Matthews 19:38, 8 Sep 2004 (UTC)
"Since finite-dimensional Hilbert spaces are fully understood in linear algebra (...)"
That's not completely true. In fact, very much is unknown even about the geometry of !
mbork 15:16, 2004 Nov 23 (UTC)
Is it really kind to give the three volumes of Dunford and Schwartz as basic reference? Charles Matthews 18:42, 23 Nov 2004 (UTC)
Hahn-Banach theorem
The error was saying that the Hahn-Banach theorem requires the axiom of choice when it doesn't. Cwzwarich 02:25, 4 December 2005 (UTC)
- Are you sure? At Hahn-Banach theorem they say that it requires Zorn's lemma, which is the same as the axiom of choice. Oleg Alexandrov (talk) 02:29, 4 December 2005 (UTC)