Wikipedia:Articles for deletion/Polynomially reflexive space


 * The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review).  No further edits should be made to this page.

The result was   no consensus. Scott Mac (Doc) 14:24, 22 February 2010 (UTC)

Polynomially reflexive space

 * – ( View AfD View log  •  )

Long-standing unreferenced tag. I searched for references and found only found two journal articles; no evidence for notability. There are two links from other articles, also in unsourced statements. An error in the definition was pointed out on the talk page 5 years ago and has not been fixed. RDBury (talk) 00:21, 13 February 2010 (UTC)


 * Keep. This article has an internal consistency that suggests that it was written by someone who knew what they were talking about.  The continued presence of defects in an article should not be considered grounds for arbitrary deletion when the subject area is not one of common expertise, particularly if proposers advance no evidence of their own competence to form a judgment.Opbeith (talk) 12:04, 13 February 2010 (UTC)
 * Whether it's correct or not or whether the author knows the subject isn't in question. Wikipedia is not a repository for current research. I included the note about the error not as a reason for deletion in itself, but as evidence that there is no one taking enough notice of it to ensure that it's accurate, which is exactly the danger the danger with non-notable subjects.--RDBury (talk) 22:02, 13 February 2010 (UTC)


 * I can't see how this is current research. This is a descriptive article which refers to another article which provides an example of what is described.  The article says quite specifically that polynomially reflexive spaces are rare but it quotes an example of a polynomially reflexive space, a symmetric tsirelson space.  At the Tsirelson space article the symmetric Tsirelson space is referred to as being polynomially reflexive.  If the Tsirelson space article is OK then this article has to be OK.  Deleting the explanation of something that another article refers to even if there is no link seems unwarranted.  Lupin did not in fact refer to an error, just to an apparent lack of clarity.  Surely it is dangerous to assume that where a subject is in a recondite area it should be deleted if there is no evidence of routine supervision.  Similarly using the number of journal articles to judge the notability of something that is in itself rare in a field that is not overpopulated seems a very unreliable tool.  Lupin did not in fact refer to an error, simply requested clarification.  You and I are not competent to judge the adequacy of the article and a lack of frequent visits seems a dangerous basis to remove information whose relevance elsewhere we are unaware of.  Have earlier, apparently informed editors, who may still be around been asked for their comments - Charles Matthews and Michael Hardy, or some of the editors who contributed to the Tsirelson space article?  This seems a wiser procedure for checking the appropriateness of deletion. Opbeith (talk) 23:17, 13 February 2010 (UTC)
 * Apologies - I shouldn't be assuming your non-competence alongside mine, however you do seem to be relying on a priori arguments. Opbeith (talk) 23:20, 13 February 2010 (UTC)
 * The deletion/inclusion criteria are set up so that a great deal of expertise is not needed. For math articles what is required is a non-trivial mention in a reliable secondary source, usually a textbook. I made a good faith effort to find such a source and none was given in the article so I have to conclude that the subject does not meet notability criteria. If you feel the subject is notable then show how it satisfies the criteria given in WP:Notability. Again, I'm not claiming Lupin's note in the talk page (and yes, it was an error - Lupin was being polite) as a primary reason for deleting the article since I would hope that lack of evidence for notability would be sufficient. The reason I included it is that it shows the subject is apparently so abstruse that no one has fixed an obvious factual error in 5 years. My understanding is that that's part of the reason the notability criteria exist and are set where they are; Wikipedia should not have articles that are so technical that only a few researchers are competent to verify them since there is too much current research going on and too few Wikipedians who would be able to ensure the material is accurate. However, you right in that including it is a form of WP:NOEFFORT so I withdraw it as a possible reason for deletion, lack of evidence of notability still being sufficient reason. On the other hand, most of your arguments seem to be variations of WP:OTHERSTUFF and WP:EFFORT which are not arguing to the basic issue of whether the article meets notability criteria.--RDBury (talk) 00:19, 14 February 2010 (UTC)


 * I think you're probably being polite and patient with me, as you you're numerate enough to be able to confirm the error. Nevertheless I think there is still an issue, in that this article aims to provide the explanation of another term which, however rare, is important in the context of part of another article whose notability I assume is not challenged.  Deleting the Polynomially reflexive space article basically marks the side road from Tsirelson space as non-existent because it's dangerous.  I would have thought there are two other more constructive options.  One is to repair the road, which may require an expert road-mender.  The other is simply to flag the road as being dangerous and advise anyone that they take it at their own risk - either as a tag or in a form of words included in the text.  The road links the Tsirelson space article to somewhere a user of that article might want to check out via the closest route first before embarking on a more complicated journey (via mathematical dictionaries, textbooks, search engines) to find the place.  The rules provide guidelines, they shouldn't obstruct the pursuit of knowledge.  Incidentally - I'm afraid the intricacies of "notability" lose me - does the removal of this term imply that the reference to polynomially reflexive spaces should be edited out of the Tsirelson space article?  And should any other references to polynomially reflexive spaces, linked or unlinked, be identified and examined as part of the deletion process?  Is there no recommendation for an overview to ensure that decisive action isn't taken on a piecemeal basis? Opbeith (talk) 09:48, 14 February 2010 (UTC)


 * I have added a reference, hope that helps. In my opinion however the article is not very clear: it is not properly explained what it means for a polynomial to be "reflexive on a Banach space". 131.211.113.1 (talk) —Preceding undated comment added 22:41, 14 February 2010 (UTC).


 * Comment: I have taken the step of asking Tsirelson, which is of course at the opposite extreme from looking at policies that are claimed to be valid for every topic under the sun. It nonetheless seems reasonable to me. Charles Matthews (talk) 12:32, 16 February 2010 (UTC)


 * Thank you. That seems an appropriate way of pursuing the issue in a constructive spirit. Opbeith (talk) 14:11, 16 February 2010 (UTC)


 * Delete, primarily as failing WP:N. As noted above, the main definition is ambiguously stated, and it is rather unclear what the subject of the article actually is (the correct definition probably involves requiring that for every N the space of complex-valued N-homogeneous polynomials from X to C be reflexive, or something similar, I am not sure). I checked MathSciNet, and the paper of Farber, given as the main reference, is cited only 8 times there since its publication in 1994. Given that the notion in question is highly technical and highly specialized, even for the experts, that does not seem sufficient to pass WP:N. Nsk92 (talk) 23:08, 14 February 2010 (UTC)
 * Change to Neutral for now. The source pointed out by Sławomir Biały actually makes it clear that the notion predates the work of Farber, and gives references to the work of others who studied this notion. Nsk92 (talk) 01:32, 17 February 2010 (UTC)


 * Comment. I do get quite a few scholar hits for "polynomial reflexivity", most of which are relevant for the subject of the article: .  Sławomir Biały  (talk) 02:21, 15 February 2010 (UTC)
 * Proposals for deletion often don't check alternative formulations, even obvious ones - eg the proposal to delete Richard C. Longworth - allegedly a "non-notable scribe" - never seemed to have looked for "Richard Longworth". The problem is compounded with non-Anglo formulations.  That's particularly dangerous where specialised, and so possibly infrequently consulted, articles are concerned, when not many people are going to be aware of the impending prospect of removal. Google and even other more specialised search engines will only produce the results you ask them to. The encyclopaedic spirit should also require insistence on a bit of lateral thinking to be a necessary component of any culling procedure. Opbeith (talk) 09:57, 15 February 2010 (UTC)
 * The onus is on the person creating the article to give references for it that show the subject is notable. If someone had to jump through all the hoops your suggesting, checking all permutations of the name in multiple languages, before doing an AfD then nothing would ever be deleted and Wikipedia would fill up with spam and nonsense. Yes it is better to find a reference if possible and I think I made a reasonable, good faith effort to find one that meets notability criteria. If you have a reliable secondary source with a nontrivial mention of the subject then add it to the article and I'll gladly withdraw the AfD. In other words, if the AfD is unfair then say it's unfair and prove it's unfair, but don't use this backhanded "Gee, there are so many articles that are unfairly put up for deletion," argument.--RDBury (talk) 13:03, 16 February 2010 (UTC)
 * Unreferenced is not a criterion for deletion, and part of the purpose of having an AfD in the first place it to attempt to turn up additional references. And as a matter of overall procedural conduct, I am reluctant to point out that perhaps WP:BEFORE was not observed very judiciously in this case.  At any rate, that particular point is now moot, as the article is now sports a reference.  So, there is only the question of notability to settle.  The Google scholar search turns up 11 relevant sources, 6 of which are in top journals.  Many of the 8 cross-references listed on MathSciNet seem to be directly relevant to the topic of the article, and some of them are in good journals.  While there is no concrete numerical criterion for notability, I should think that this one passes.  Therefore I am leaning towards keep.  Sławomir Biały  (talk) 14:03, 16 February 2010 (UTC)
 * We seem to be using different criteria for notability. WP:SECONDARY gives a link to the Ithaca College Library to explain the difference between research articles and survey articles. Research articles are considered primary research and therefore not evidence of notability as Wikipedia defines the term, even if they do appear in top journals. Survey articles are allowed but I didn't see any in the Google link you gave, nor did I find any in my own search. Please don't assume that I did not perform a good faith search for sources simply because your interpretation of notability guidelines differs from mine. WP:BEFORE states "When nominating due to sourcing or notability concerns, make a good-faith attempt to confirm that such sources don't exist," which I did. It does not require proof beyond a reasonable doubt that there are no such sources or that I spend more time looking for them than it took to create the article in the first place. WP:YFA states "Gather references both to use as source(s) of your information and also to demonstrate notability of your article's subject matter," which is why I claim that the onus of proving notability falls on the person who created it, not on the person attempting to delete it.--RDBury (talk) 22:00, 16 February 2010 (UTC)
 * Actually, I think you are asking for a bit much here. The basic principle of WP:N and all other notability guidelines is that sources cited be independent from the subject (rather than necessarily be secondary in the technical sense of WP:SECONDARY). As WP:N puts it: "If a topic has received significant coverage in reliable sources that are independent of the subject, it is presumed to satisfy the inclusion criteria for a stand-alone article." Thus for a mathematical theorem proved by a particular author, I would consider research papers by other mathematicians that significantly use or generalize that theorem to be valid examples of independent coverage, even if no survey papers are available. Similarly, if someone introduces a particular mathematical notion, and other researchers start actively using and studying this notion in their papers, I would consider that to be perfectly good examples of independent coverage, even if nobody has bothered to write a survey article about it yet. I think that for notability purposes the real question is the extent and depth of independent coverage available. My impression was that in this case the amount and depth of such coverage (by people other than Farber) was not sufficiently significant, but if evidence is presented to the contrary, I am quite prepared to change my mind. Nsk92 (talk) 00:08, 17 February 2010 (UTC)
 * I understand your position, but disagree with the subjective assessment that "the amount and depth of such coverage (by people other than Farber [sic]) was not sufficiently significant". It might be better to generalize the subject of the article to some degree, even as much as "polynomial properties of Banach spaces".  The literature review here clearly indicates that polynomial reflexivity (and things very closely connected to it) have been studied by quite a few researchers independent of the subject, some of them (like Sean Dineen) being quite distinguished in the field.  So I'm just not seeing the same lack of amount and depth, based on my own cursory gestalt of the available sources.  Sławomir Biały  (talk) 01:02, 17 February 2010 (UTC)


 * Keep. See my comments above.  Sławomir Biały  (talk) 14:03, 16 February 2010 (UTC)


 * Merge. Why choose between keep and delete? The topic is probably too narrow and special for an article, but appropriate for a section in another article (near the end, since technical). Specifically, I propose to merge it into polynomials on vector spaces, for now a purely algebraic article. The (good) Vector space article contains analytic sections; also "Polynomials on vector spaces" could contain. I've expanded the article a bit, so that its relation to polynomials is more clear now. And of course, a redirect page should be made here. Alternatively, it could be merged into Reflexive space or even Banach space. Boris Tsirelson (talk) 15:46, 16 February 2010 (UTC)
 * Comment. Could there be scope for a new article, something like "Polynomial properties of Banach spaces", that includes reflexivity?  Sławomir Biały  (talk) 01:02, 17 February 2010 (UTC)
 * Comment. Then maybe "Polynomials and analytic functions on Banach spaces", or even "Functions on infinite-dimensional spaces"? Boris Tsirelson (talk) 07:05, 17 February 2010 (UTC)


 * Comment - I'm very happy to withdraw my own Keep above in favour of whatever the people competent to judge decide between them now that the matter has received thorough consideration, for which Thanks. Opbeith (talk) 17:21, 16 February 2010 (UTC)
 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.