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On Reference for invariance of essential spectrum under relatively compact perturbations, Michael Renardy voted to close with the comment "This site should not become a shortcut to substitute for literature searches", and it seems at least two others are of the same opinion. Respectfully, I'm not sure I agree, either in the context of this question or in general, and I thought I would solicit the community's input. Indeed, I thought this was the whole point of the tag, and a major part of what makes this site an asset to the community.

Searching the literature for a specific result is a tedious and often unrewarding task, especially for a junior researcher or someone looking for results outside their own area of expertise who may not even know where to begin. Online search tools are not very good at this: the desired paper may state the result in different language, or prove a generalization. The situation gets much worse if one has to search for symbols.

It's a time-honored tradition to shortcut this drudgery by asking an expert colleague whom you suspect might know immediately where to find your result, or at least where to start looking. But not everyone has an expert colleague down the hall, which to my mind is exactly the reason why MO was started.

There's a limit, of course: we want questions which are "research level", which by consensus seems to be roughly defined as "beyond a standard first-year graduate course". I think the question at hand certainly meets that standard: I have a Ph.D. and what I like to think is a working knowledge of basic functional analysis, and I don't have any idea where to find the requested result.

I don't see such questions as making a disrespectful demand on the time of others, either; a reference request can be answered in seconds by someone who knows where to find what's wanted, and everyone else can shrug and move on. Many people here invest much more time in writing detailed answers to complicated questions. I personally would gladly take the time to answer this question if I knew an appropriate reference, and would do the same for any other reference request within my limited expertise.

I'd appreciate hearing any other thoughts.

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    $\begingroup$ I was hoping someone would weigh in by now, but the question seems unobjectionable to me too (and we see reference requests all the time). There are occasional responses to questions that suggest the expectation that the OP has already done a little homework before bringing a question to MO -- not a bad rule of thumb -- and maybe the commenter thought that here. Not sure. $\endgroup$ – Todd Trimble Feb 24 '14 at 12:51
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    $\begingroup$ I agree that reference requests should be welcome on MO, and to me the question seems fine. $\endgroup$ – Thomas Rot Feb 24 '14 at 13:18
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    $\begingroup$ I know in certain other stackexchange forums, questions will be quickly closed unless they show research on the part of the asker. $\endgroup$ – Gerald Edgar Feb 24 '14 at 14:30
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    $\begingroup$ @GeraldEdgar: I think the question at hand passes that test, too. The asker specifically mentions one reference already found and explains why it's not what he/she wants, and describes having found a similar result in several other places. It looks to me like research has been done but without success. $\endgroup$ – Nate Eldredge Feb 24 '14 at 15:27
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    $\begingroup$ Rumsfelds Theorem (there are known unknowns, and unknown unknowns) immediately springs to mind. Example: No amount of search could have led me, an amateur, to "Burnside obstruction to the Montesinos-Nakanishi 3-move conjecture" (only sheer dumb luck and the fact that he's the P of HOMFLYPT). Hey, couldn't he named the paper "Reddmanns skein relation sucks because the recursion won't get started for complicated knots"? :-) And thus I'm deeply indebted for any reference MO digs up for me. Even if I don't understand a word of it (which is likely :-) $\endgroup$ – Hauke Reddmann Apr 7 '14 at 14:23
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Many MO questions, not just reference requests, could be answered by a literature search. Yet, a main point of having this site is to avoid having somebody spend a lot of time searching for something that somebody else just might know from the top of their head.

However, it should also be note that the emphasis here is on "a lot." Before asking a question on this site, any question not just reference requests, one better should make some effort oneself to find the answer by oneself, and this is also in the FAQs, more specifically in How to write a good MathOverflow question? (under "Do you homework")

Thus, this site should be used to avoid long literarture searches, yet not to avoid all literature searches.

It is difficult for me to tell, this not being my field, how hard it is to find the answer to that particular request linked in OP. For me, as a non-expert, the request seems well-written, especially I like that it mentions the related result for Hilbert spaces. And, I would thus assume, or at least give the benefit of the doubt, that OP made some effort beforehand and thus find this particular question a rather good example for a reference request question.

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    $\begingroup$ In spirit, if not in letter or semantics, this question is a duplicate of meta.mathoverflow.net/questions/1381/… . I think that MathOverflow is not a reference desk, but is the next line of resource after the reference desk has been approached. I think developing and communicating a tighter analogy will make the definition of the purpose of MathOverflow clearer to that portion of the community that appreciates such distinctions, and might help in day-to-day operations as well. Gerhard "Not Asking For Question Closure" Paseman, 2014.02.24 $\endgroup$ – Gerhard Paseman Feb 24 '14 at 19:14
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I am in favor of (prudent) use of MathOverflow as a tool to find underexposed content such as proofs of "folk theorems" and alternative proofs of standard facts. An advantage of this use is that replies at MO often come with meta-information which is worth archiving (informed opinions, equivalences between approaches, errata and historical information); I would even expect the occasional complete proof being posted in response to a reference request (which, in my eyes, is a positive-sum outcome). I'm wondering if this discussion would have emerged at all if question 158438 hadn't been tagged reference-request; the author was merely asking for a proof different from a proof he didn't like. I have done so several times and I don't remember anyone criticising me for not doing my google homework. When I look at questions tagged reference-request, I'm seeing many that could just as well work without that tag. (I personally am far more annoyed by the "give me a reference, not a proof" type of question, but that seems to be mercifully rare.)

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"Searching the literature for a specific result is a tedious and often unrewarding task"

Therefore it is better if someone else does this for you?

I think that the attitude to the "reference request" should be the same as to other MO questions: they must be "research level" questions. Ideally, you do a search yourself, using all common tools, and in a really difficult case, you ask for a community help. Literature search, like solving a mathematical problem, could be a non-trivial task, even with all these Internet tools. Many answers to this sort of questions in MO can serve as evidence of this.

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    $\begingroup$ It's not so much that you're asking other people to search the literature, but rather that you're asking if someone knows something off the top of their head. It can be hard to know how to look something up in an area you don't know very well (though obviously it is an inappropriate question if e.g. googling the question title immediately turns up the answer or something). $\endgroup$ – Andy Putman Mar 1 '14 at 18:23
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    $\begingroup$ @AndyPutman: Yes, that was exactly my point (which I tried to explain in the paragraph following the one from which Alexandre quoted). $\endgroup$ – Nate Eldredge Mar 1 '14 at 18:31
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    $\begingroup$ Perhaps a "collective memory" tag could be established to indicate the kind of search that can't be done by keyword alone, and for which a brief pointer to the literature would suffice. My second question mathoverflow.net/questions/134826/… would likely have benefitted from such a tag . $\endgroup$ – The Masked Avenger Mar 2 '14 at 21:16
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    $\begingroup$ @TheMaskedAvenger what would be gained from having such a tag? In which way would this be an improvement over having just reference-request? Or, what should be the precise difference? $\endgroup$ – user9072 Mar 3 '14 at 1:00
  • $\begingroup$ @quid, I messed up my response and deleted it. The intent is that a vague but suggestive memory might answer this new type: only a bibitem or equivalent will answer a reference request. $\endgroup$ – The Masked Avenger Mar 5 '14 at 22:00
  • $\begingroup$ In particular a bibitem to me carries an air of certification; a half remembered event does not, yet may be effective through suggestion. $\endgroup$ – The Masked Avenger Mar 5 '14 at 22:01
  • $\begingroup$ @TheMaskedAvenger thanks for the explication. There might be room for finer nuances in the large reference-request tag, which I agree is not optimal; the then mildly controversial creation of textbook-recommendantion comes to mind. Though I see some issues with the particular name you propose for the tag; not only but also as a tag should typically indicate what the question is about. If you want to follow up on this perhaps create a q on it or we could chat about it in the editors' lounge. $\endgroup$ – user9072 Mar 5 '14 at 22:56

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