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article, the purpose of wikipedia is not to "teach" by explicitly writing down the most minute details of a subject in a fully deductive fashion (to the point of making it nearly inaccessible to anyone except the most motivated persons with already a background in the subject). Instead, it is to present a coherent and accessible overview of the topic, and refer to referenced sources for anyone interested in exploring further. Again, thank you!
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fact that it generates the projective topology just characterized in the universal property; (3) a sentence saying that the tensor product of seminorms which are also norms is a norm, and that this construction therefore carries over to normed spaces. I'll split the post here so I can sign and then give my suggested text.
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I am going to remove the subsection of "Examples" with this title, and am starting a discussion in case there is an objection to this. There are at least two possible arguments to remove this subsection. First among these is that this appears to be more of a result about nuclear spaces than about the
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a section called "Definitions" before "Properties." This will consist of: (1) the universal property currently in "Properties," characterizing the projective tensor product for all locally convex topological vector spaces; (2) a statement of the construction of the tensor product of seminorms and the
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Thanks for replying. I think that the extra detail in the section
Projective norms in the old revision here is textbook-like elaboration that does not constitute a summary. The sentence starting with "Given..." and ending with a sum of simple tensors is a "trivial" derivation from the definition of
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It looks as though this section is based on the first full paragraph on p. 435 and the first full paragraph of p. 438, of Trèves. The problem comes from the fact that these two paragraphs, in their entirety, are closely paraphrased, not summarized. So, although you asked for specific sentences that
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I want to personally thank you for this major rewrite. Functional analysis is not exaclty my area of expertise, but I want to say that the result is a *lot* more readable and accessible than the previous version. As has been discussed previously a few times with the previous main editor of this
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Hi
PatrickR2, thank you for the compliment about some of my contributions here. I'd rather not involve myself in any past content disagreement you seem to be describing, but hope anyone who would have otherwise disagreed with recent changes to the page will find my reasoning above persuasive.
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Respectfully, my opinion is that this is mostly unencyclopedic restatement of facts that appear as propositions and problems in the textbooks. If a way could be found to present some of it in a more natural and encyclopedic way, I would be glad to have it in the article.
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Sections "Seminormed spaces" and "Examples" paraphrase too closely their respective sources. Added the relevant notice for now. I might try to shorten them down into a couple sentences and put them elsewhere later but if someone else wants to then go ahead.
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I am splitting the "Bibliography" section into a "References" section (for sources cited in the article) and "Further reading" section, and removing the references that, based on their tables of contents and indexes, don't talk about this topic.
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might be argued, and I know that it is especially difficult to summarize mathematical statements rather than paraphrasing them. But I do think that there are opportunities to summarize more here (rather than paraphrase), which means that
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are problematic, the problem doesn't come from the way the paraphrasing is done in any particular sentences independently; instead, it comes from the volume of text that is closely paraphrased, as a whole. Now, I see how, as you say,
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What do you think? I think this reduces paraphrasing to a minimum, collects together the definitions, and gets rid of some less important detail. And, as this reflects, having looked at more sources, I am open to reintroducing the
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regarding section
Seminormed spaces, followed by my suggested change for how to remedy this issue and reduce the overall level of technical detail on the page. Later, I'll have a suggested change for the examples section.
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doesn't apply. Namely, Prop. 43.1 is an elaboration of what precedes it in that paragraph in the book. Restating it is not necessary to summarize the essential content of the paragraph (namely, that a seminorm on
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about projective norms, which I think is important to understanding projective tensor products. I suggest restoring some of this information. Your thoughts?
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projective tensor product itself—indeed, that is the way that the only source for the example, pp. 179–184 of
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sections "Normed spaces" and "Seminormed spaces." These will be incorporated in a new section preceding "Properties."
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subscripts. (I originally removed them because the source I was familiar with didn't use them.) Thanks for reading.
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is induced by the family of their tensor products." I will do something similar when I give the suggested new text.
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the norm. The next one is exactly what you would expect for the completion. The next one (with
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Thank you for your work and my apologies for the lateness of my reply (I've been busy). You
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To summarize the content on p. 438, we could say something like, "when the topologies on
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be locally convex topological vector spaces. Their projective tensor product
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are induced by families of seminorms, the projective topology on
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Since you said to go ahead and make my changes, I will do that.
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Here is suggested text for the new "Definitions" section:
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1169:. The projective topology on
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1425:{\displaystyle \lambda _{i}}
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640:continuous
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1637:ByVarying
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1462:ByVarying
1439:ByVarying
1375:ByVarying
368:ByVarying
166:ByVarying
1089:balanced
1067:, where
1021:for all
934:given by
1396:Mgkrupa
1087:is the
634:to the
183:Mgkrupa
139:on the
30:C-class
839:, and
356:Remove
36:scale.
1238:When
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686:When
516:, if
1643:talk
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1547:OCLC
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1298:and
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390:Let
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1041:in
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1657::
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994:∈
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616:Φ
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554:×
525:Φ
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185::
181:@
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42::
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