Wikipedia:Articles for deletion/Nuclearity


 * 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 Redirect to Nuclear. - 2/0 (cont.) 08:03, 13 December 2009 (UTC)

Nuclearity

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The article only describes what the topic is about, not what it is or where it relates to standard methods in mathematics. If properly explained, and the name is adequately sourced, I'll withdraw the nomination. — Arthur Rubin (talk) 00:04, 4 December 2009 (UTC)


 * WP:CSD (insufficient context) was declined. Although I don't agree with the reasoning, I'm not going to reinstate the tag.  — Arthur Rubin  (talk) 01:35, 4 December 2009 (UTC)


 * Delete As I explained on Arthur Rubin's Talk page, I declined the speedy deletion because I think the article provides sufficient context to survive A1, but I think the article should be deleted unless a knowledgeable editor can add a basic statement of what the subject is (i.e., "Nuclearity is the property of ..."). (Well, as basic as possible, given the relatively obscure subject matter.) — Malik Shabazz Talk/Stalk 01:51, 4 December 2009 (UTC)


 * Redirect to nuclear space.  Sławomir Biały  (talk) 01:59, 6 December 2009 (UTC)  In light of comments by User:Mathsci, I withdraw this suggestion.   Sławomir Biały  (talk) 16:16, 6 December 2009 (UTC)


 * Redirect to nuclear space. The article is so vague about what it's supposed to be about that it's hard for me to tell if it's close to the intent of the article creator, but in general the names of articles on properties should be the property plus the noun if applies to rather than an abstracted version of the property (which is likely to be a neologism). For example Bounded set rather than boundedness, connected space rather than connectivity, etc. So a redirect to 'nuclear something' is warranted and 'nuclear space' seems as good a candidate as any.--RDBury (talk) 05:23, 6 December 2009 (UTC)
 * Rename article to Nuclear C* algebra and rewrite properly. The definition of a nuclear C* algebra A is that there is only one C* tensor norm on $$A\otimes B$$ for any other C* algebra B, namely the spatial norm obtained by taking faithful representations on Hilbert spaces. The theory of nuclear spaces does not contain the theory of nuclear C* algebras in any way at all, contrary to what has been stated above by User:Sławomir Biały. The subject is linked to that of operator spaces and the more general class of exact C* algebras by the work of Eberhard Kirchberg; it has important applications in K-theory. As Alain Connes showed, a separable C* algebra is nuclear iff the von Neumann algebra generated by any representation is hyperfinite, a result which was a corollary of his his classification of injective factors for which he won the Fields medal in 1982. This major result is not recorded in the article. The originator of the article, User:Henry Delforn, whom I have come across before, does not seem to know the subject very well. A proper article could certainly be written on the subject. The classification of (simple) nuclear C* algebras is described in detail in the book of Mikael Roerdam in the Springer series "Encyclopedia of Mathematical Sciences". So I agree with Arthur Rubin that the article should be renamed to nuclear C* algebra and completely rewritten with a proper set of sources (several books and sets of lecture notes). The Roerdam book also contains references to lecture notes on exact C* algebras by collaborators of Kirchberg. (A C* algebra A is exact if the spatial tensor product of it with a short exact sequence of C* algebras remains exact. There is an equivalent characterization in terms of operator spaces.)  The subject is also covered in the encyclopedic three volume Springer series of Masamichi Takesaki. Mathsci (talk) 15:51, 6 December 2009 (UTC)
 * If the topic really is valid then the operative question is whether there is anything in the current article that can be salvaged or is it better to just start from scratch. In the former case, a rename would be appropriate. In the latter then a delete would be appropriate since you can always start the new article with the correct name.--RDBury (talk) 06:21, 7 December 2009 (UTC)


 * Comment If there are indeed two separate concepts of nuclearity then this page should become a disambiguation page pointing to Nuclear space and Nuclear C* algebra. Quotient group (talk) 21:45, 6 December 2009 (UTC)
 * Comment My friend User:R.e.b. has in fact just started a new article Nuclear C* algebra using some of my suggestions. (It might also be useful to add the books of Effros & Ruan and Pisier on operator spaces.) A disambiguation page should also contain a reference to nuclear operator, sometimes used instead of the more common term trace class operator in the context of Hilbert spaces. Mathsci (talk) 22:23, 7 December 2009 (UTC)

 Please add new comments below this notice. Thanks, JForget  21:33, 11 December 2009 (UTC)
 * Relisted to generate a more thorough discussion so consensus may be reached.


 * Redirect to Nuclear, a pre-existing disambiguation page. I have added the three occurrences of "nuclear" in mathematics, all of which are related to tensor products in functional analysis: Nuclear space, Nuclear operator and Nuclear C*-algebra. The current article serves no purpose at all. Mathsci (talk) 08:52, 12 December 2009 (UTC)
 * Since this seems to be the only possible outcome at present (because of the above discussion, the creation of Nuclear C*-algebra and the changes to Nuclear), I have changed Nuclearity to a redirect to Nuclear. Mathsci (talk) 11:46, 12 December 2009 (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.