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This tag is used if a reference is needed in a paper or textbook on a specific result.

0 votes

About the trace class operators and their motivation

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 …
Stefan Waldmann's user avatar
2 votes

Properties of the total variation norm on space of totally finite measure (from Bogachev)

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 …
Stefan Waldmann's user avatar
2 votes

Reference for : a Fréchet nuclear space is Montel

Maybe not in a single theorem, but you can go for Cor1 in Section 33 and Cor3 in Section 50 in Treves book.
Stefan Waldmann's user avatar
4 votes

Reference: Learning noncommutative geometry and C^* algebras

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 …
Stefan Waldmann's user avatar
4 votes

Commutator formulas in a universal enveloping algebra

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 …
Stefan Waldmann's user avatar
9 votes

Dimensional Analysis in Mathematics

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 …
Stefan Waldmann's user avatar
14 votes

Deformation Quantization

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 …
Stefan Waldmann's user avatar
11 votes
1 answer
671 views

Analysis and finitely generated groups

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 …
Stefan Waldmann's user avatar
5 votes

Morita equivalence for *-algebras

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 …
Stefan Waldmann's user avatar
8 votes
Accepted

Is there dual space of the distributions $\mathcal{D}'(R)$?

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 …
Stefan Waldmann's user avatar
3 votes

graded generalization of the Moyal–Weyl product

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 …
Stefan Waldmann's user avatar
6 votes

analysis over non-Archimedean ordered fields

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 …
Stefan Waldmann's user avatar
5 votes

Relation of the first Hochschild cohomology and the outer automorphism group

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 …
Stefan Waldmann's user avatar
16 votes
Accepted

Hodge decomposition of smooth n-forms: is it an isomorphism of topological vector spaces?

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 …
Stefan Waldmann's user avatar