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Maybe an even more elementary argument than the one of Tobias: The continuity of all involved operators is easy: simply all differential operators with smooth coefficients between sections of vector b …

Unfortunately, there is no real textbook on DQ around. One has Fedosov's book on his construction of star products including a detailed exposition of his index theorem. There is a chapter on DQ in t …

Dear all, this is perhaps a bit a vague question, but some references would already be very helpfull. So let $G$ be a finitely generated group and choose some finite set of generators. This allows to …

Dimensional analysis can be viewed as the study of graded objects in algebra. The grading then corresponds to "counting the units" in a precise way. There are of course many examples and I believe tha …

Well, that depends on what topology you want to put on the space of distributions. The weak$^*$ is probably not really the one you would like to take. Instead, the strong dual might be more useful. Th …

Well, there seems to be a lot of literature. I have encountered similar questions once when discussing problems in deformation quantization. here the ordered field is simply the field of formal Lauren …

Usually I do not want to make to much of advertisement for my own stuff, but here it matches only too well: in a series of papers Henrique Bursztyn and myself developped the theory of Morita equivalen …

Another easy counter-example: take $X = \mathbb{N}$ as discrete topological space and $R = C(X, \mathbb{R})$ as continuous functions on it. These are just all functions. Equivalently, you can view the …

For $C^*$-algebras in general, there are many textbooks. Famous names are e.g. the two volume book by Kadison&Ringrose or the (by now somehow old but still very nice) book by Sakai. I also enjoyed the …

This is probably not yet a final answer but may shine some additional light on the problem: For simplicity, I assume that $L$ is finite-dimensional and defined over the reals (for some other field of …

Yes, it's just putting signs correctly. Martin Bordemann has a preprint from the 90s where he adapted Fedosov's construction in the graded setting. If you are only interested in the flat situation thi …

Maybe not in a single theorem, but you can go for Cor1 in Section 33 and Cor3 in Section 50 in Treves book.

Let me just give a simple counter-example to your equation (1): take the real line as space (any metric space with at least two points will do) and use the delta measures $\delta_1$ and $\delta_2$ at …

As a further reference you can also consult the locally convex analysis monograph of Jarchow. A very comprehensive book, I like it a lot: it has some sections on $p$-summable operators also beyond the …