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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 …

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 …

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 …

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 …

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 …

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 …

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 …

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

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 …

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 …

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 …

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 …

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 …