Talk:Continuous dual space

GA review for Duel Space

The GA review for dual spaces contained a quality critique of this article. I'm reproducing it below

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I have reviewed the article having regard to the guidelines set out in Wikipedia:What is a good article. I have reached the following conclusions:

1. The article is largely well written. In particular, the first half dealing with algebraic duals is clear and should be understandable also to a reader with limited background in abstract algebra provided that he/she is willing to follow the links to the basic definitions. However, the second half dealing with continous duals is not quite yet up to the same standard. Partially this issue has to do with the unclear scope of the subject matter covered in this sections (referred to in 3.2 below). Specifically the subsection Further properties is still more of a stub than a well-written section. In addition, there are undefined technical terms (e.g., anti-isomorphism is neither defined nor linked elsewhere).
2. The article is mostly factually accurate. There are no issues with the first half dealing with algebraic duals (except for a slightly misleading statement in the note: weaker axioms than the full axiom of choise suffice to show that R^N has a basis; while this may be already splitting of hairs, I would propose wording like "the (usual) proof makes use of the axiom of choice"). However, somehat misleading statements are made in the second paragraph of the Further properties subsection of the second section: the statements therein appear to apply to all topological vector spaces, while they are not true in such generality (e.g., for a non-Hausdorf space the canonical mapping to the bidual is not injective). They would hold for normed spaces, and perhps the intention was to continue discussing only Hilbert spaces. This should be easy to fix. Worse issue is that the article does not cite any references. Pointers to at least a few good textbooks and references should be given.
3. The article is not broad in its coverage. This is largely due to its ambitious scope to cover both algebraic and topological duals. My observations are as follows:
   1. The first section fares quite alright as an encyclopaedia article on algebraic duals of vector spaces. More context for the duality (such as role of algebraic duality in topological (cohomological) duality theorems) could still be added. However, duality for vector spaces is a special case of duality for modules, and treating them in two separate articles would lead to duplication of same constructs, results (partially) and proofs. Keeping duality for vector spaces separate could be justifiable by (i) willingness to keep it together with topological duals or (ii) to avoid introducing too much additional terminology to the vector space case. Either way, the fact that this is a special case should be mentioned and elaborated here or linked to a new article.
   2. The second section is not ready in terms of coverage even for s short enecyclopaedia article. There is clearly an issue of how broad categories of topological vector spaces to cover — the article begins by encompassing all topological vector spaces, then moves to normed spaces and Hilbert spaces without a warning. The article does not mention the question of which topology to choose for the dual if the space is not normed. And even for normed spaces there are alternatives to the strong topology, which is not mentioned (although weak dual mentioned briefly at the very end). A problem from the viewpoint of editing the article is that duality for general topological vector spaces is not entirely straightforward, but leads to rich structures and quite theory. There could be a case for a smaller scope for this article, but at least that would require that the general (and by no means "academic"!) case be mentioned and linked.
4. Neutrality, stability and images are in good shape.

In summary, I have found the article to be good in many respects. However, the issues above are such that I am led to fail the GA nomination for now. I considered "On hold" status instead, but I find it hard to assume that the issues relating to the broadness of coverage on topological duals could be resolved in a week. One option would be to split the article into algebraic and topological duals, in which case the half on algebraic duals could be developed to the Good article level fairly quickly. However, the topic appears to have been discussed above, and reaching consensus on such a decision could take time and likely not be completed in a stable manner in one week either.

As a final note, I think this article is clearly capable of growing into a Good article status and beyond with some more editing.

Stca74 20:48, 11 May 2007 (UTC)

Merge proposal

I propose to merge this article to Dual space. The two articles deal with closely related concepts so that reading them together will be helpful for understanding. Both articles are relatively short in lengths, especially Continuous dual space. --Acepectif 07:59, 24 August 2007 (UTC)

It appears that someone has gone ahead and merge anyway. Silly rabbit (talk) 22:26, 1 January 2008 (UTC)

No, the reason they look so similar is because this article was created by copying the text from the dual space article. I think we should have separate articles on the algebraic and continuous duals (to reduce confusion, and because one is algebra and the other is analysis), and have a short article at dual space explaining the difference and how they relate to one another. --Zundark (talk) 22:40, 1 January 2008 (UTC)

Yes, a bit of forensic investigation revealed that to be the case. I don't feel strongly one way or the other, but the current state of affairs is unacceptable: this article is a duplicate of part of the dual space article, except for some corrections over at dual space that I (and others?) have made at one point or another. Silly rabbit (talk) 22:43, 1 January 2008 (UTC)

Content fork

I have replaced the page with a redirect to dual space until any editing disputes can be resolved. It seems that the content fork was not done with community support. If it was, the job was badly botched. I do not object to splitting the article dual space, but it has to be done properly. Rather than leaving the old information there verbatim, use summary style to summarize the key features of the continuous dual space article. Silly rabbit (talk) 18:50, 3 January 2008 (UTC)