Here's one piece of evidence that "Behind the table" is an actual 
subject in the sentence under discussion: the verb "is" moves in front 
of it to form a yes-no question:

Is behind the table where I looked?

Contrast that with the case with an unquestionable instance of inversion:

On the table is my book.
*Is on the table my book?

On 9/3/2010 3:23 PM, John Dews-Alexander wrote:
> Good points. Maybe I can do better.
>
> Subject: /Behind the table/ is where I looked.  This could be a sentence
> pattern 1 (Subject, being verb, adverb of Time/place), just in a
> reversed syntax.  “behind the table” would then be an adverbial
> prepositional phrase. I suppose this depends on whether you base
> function on a generative concept of language; I tend to base function on
> the pattern as it is exists, not the prototypical form. As your exchange
> with Larry proves, the form is context-driven, but I think that is the
> point. Prepositional phrases can function nominally if context calls for
> it. Perhaps a better example would be "Behind the table is filthy."
>
> Subject Complement: The best part of my day is /after lunch/.  Same as
> above, with “after lunch” being the adverbial prepositional phrase
> answering the question “when.” I don't see how this PP is adverbial. If
> you changed the pattern, it could be the subject. If you remove it you
> get "The best part of my day is." (?). Isn't this the subject complement?
>
> Direct Object: Don't nose about /in my business/.  “In my business”
> would seem to be an adverbial prep phrase answering the question
> “where,” following the phrasal intransitive verb “nose about.”  I think
> you're right with that example. But what about "Jane painted in the
> bathroom." An adverbial would describe how Jane paints, like "Jane
> painted with smooth strokes." But "along the trim" describes /what/ she
> paints, not how she paints -- isn't that the function of the direct object?
>
> Object Complement: I bought the best gift /at the party. /(could be
> adjectival depending on analysis)  there are two kinds of object
> complements, one adjectival and the other nominal.  I could see “at the
> part” as an adverbial, as a peripheral adjectival, or as an essential
> adjectival for a pattern 9 sentence, but I can’t see it as a nominal
> object complement. Again, I see your point. Maybe a bad example. What
> about this one: "Children often consider the scariest time of day during
> the night." I'll admit it is a stretch and probably elliptical, but if
> we take it as it is, could it be a nominal object complement? Maybe not
> so I could probably concede that one.
>
> Indirect Object: You might want to give /inside the car/ a good cleaning
> as well.  This may be used in informal speech (I think I’ve heard this
> actual phrase), but in more formal speech, of course, it would read “you
> might want to give THE inside OF the car a good cleaning as well.”
> Point taken in informal speech, though. I agree that this is informal
> but not by much. The dialectologists may know better than I; perhaps it
> is moving toward standard.
>
> Telling my students that prepositional phrases are never used as
> nominals is one of the few absolutes I have left to give them—I’m loathe
> to give it up. I understand completely. I tell my students the same
> thing and warn them against those who come bearing a multitude of rules
> and absolutes. When we do find a rule that works, we hold on for dear life!
>
> John
>
> P.S. If anyone can't see color in their emails, I apologize now for the
> mess above!
>
>
>
>
>
> On Fri, Sep 3, 2010 at 2:11 PM, Joshua D. Hill <[log in to unmask]
> <mailto:[log in to unmask]>> wrote:
>
>     John,
>
>     Some of these could be analyzed differently.
>
>
>     Subject: /Behind the table/ is where I looked.  This could be a
>     sentence pattern 1 (Subject, being verb, adverb of Time/place), just
>     in a reversed syntax.  “behind the table” would then be an adverbial
>     prepositional phrase.
>     Subject Complement: The best part of my day is /after lunch/.  Same
>     as above, with “after lunch” being the adverbial prepositional
>     phrase answering the question “when.”
>     Direct Object: Don't nose about /in my business/.  “In my business”
>     would seem to be an adverbial prep phrase answering the question
>     “where,” following the phrasal intransitive verb “nose about.”
>     Object Complement: I bought the best gift /at the party. /(could be
>     adjectival depending on analysis)  there are two kinds of object
>     complements, one adjectival and the other nominal.  I could see “at
>     the part” as an adverbial, as a peripheral adjectival, or as an
>     essential adjectival for a pattern 9 sentence, but I can’t see it as
>     a nominal object complement.
>     Indirect Object: You might want to give /inside the car/ a good
>     cleaning as well.  This may be used in informal speech (I think I’ve
>     heard this actual phrase), but in more formal speech, of course, it
>     would read “you might want to give THE inside OF the car a good
>     cleaning as well.”  Point taken in informal speech, though.
>
>     Telling my students that prepositional phrases are never used as
>     nominals is one of the few absolutes I have left to give them—I’m
>     loathe to give it up. J
>
>     J. Hill
>
>
>      > wrote:
>
>     Dear List,
>
>     Does it make sense that a prepositional phrase can be used
>     nominally?  If it makes sense to substitute "that," "this," "it," or
>     some other pronoun for the prepositional phrase, could it make sense
>     to call a prepositional phrase a direct object?
>
>     For instance: in <he told his friends of the peculiar weather>, does
>     it make sense to call "friends" the indirect object and "of the
>     peculiar weather" the direct object?  In <he told his friends the
>     truth> would "friends" be the indirect object and "truth" the direct
>     object?  In <he told his friends> is "friends" a direct object, or
>     an indirect object with an implied direct object? In <he told the
>     truth> is there an implied indirect object, those who were told? In
>     <he told the truth to his friends> is "truth" the direct object and
>     "friends" the indirect object in a prepositional phrase? In <he told
>     his friends about the truth> is "friends" the indirect object and
>     "about the truth" the direct object? In <he told his friends that
>     the truth can be found> is "that the truth can be found" a clausal
>     direct object?  How else could these be analyzed?
>
>     Thanks for your help,
>
>     Scott Woods
>
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