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5h
comment a naive question: is the category of moniods cartesian closed? Why?
@Oskar How is this a duplicate of a question about commutative monoids, when it is about not-necessarily commutative monoids?
23h
comment AQA A Level Normal Distribution
Dear Dargenor, this is not the appropriate place to get help with A-Level Maths (for more explanation why, please see the information in mathoverflow.net/help )
1d
comment What is a foliation and why should I care?
Speaking as a functional analyst, +1 for the first sentence :)
1d
comment Nonseparable Hilbert spaces
Related to your example 2: there was some recent work of Ando and Haagerup on ultrapowers arxiv.org/abs/1212.5457 which I think made use of spatial representations of these ultrapowers at various points. Just as with the Calkin, faithful representations of these ultrapowers must live on non-separable Hilbert spaces
1d
comment Ideal structure of group $C^*$-agebras
Or if $C_r^*({\bf Z})$ is too easy an example, how about $C_r^*(H_3({\bf Z}))$, where $H_3({\bf Z})$ is the 3-dimensional Heisenberg group over the integers? There was an old article (paywall access I'm afraid) of Anderson and Paschke which looked at this algebra and related objects: math.uh.edu/~hjm/vol15-1.html
1d
comment Ideal structure of group $C^*$-agebras
For instance, since it sounds like you are a newcomer to the world of group Cstar algebras, you should read about the fact that the reduced Cstar algebra of the free group on two generators is simple, as this will give you some flavour of why it is usually hard to deduce properties about the ideal structure of $C_r^*(\Gamma)$ from group-theoretic properties of $\Gamma$.
1d
comment Ideal structure of group $C^*$-agebras
I'm afraid your question is still too broad; please actually provide some examples of the kinds of groups you want. By examples, I mean concrete examples, of particular groups. Every theorem about a general kind of group implies a theorem aout a particular example; in my opinion, as a researcher, if you don't know any examples of those kinds of groups, you need to find them and learn about them
2d
comment Is the module action $M\times M^*\to M^*$ jointly continuous?
@NikWeaver Of course. Sorry, lack of sleep and coffee today. I think I was getting mixed up with some issue in my head to do with completed tensor products
2d
comment Ideal structure of group $C^*$-agebras
While your question is a natural one to start with, I have voted to close because in its current form the question seems too broad to get effective answers (as opposed to people just googling for titles of articles that sound like they're relevant). If you could produce a more focused question, perhaps telling us which groups you wish to study, then I think your question would be fine.
2d
revised Ideal structure of group $C^*$-agebras
deleted 2 characters in body; edited title
2d
comment Ideal structure of group $C^*$-agebras
In general it will be very complicated. I assume you mean reduced group Cstar algebras of discrete groups, in which case these algebras can often be simple. Important examples to have in mind are: the group of integers ${\bf Z}$; and the free group on two generators $F_2$.
2d
comment Is the module action $M\times M^*\to M^*$ jointly continuous?
@NikWeaver oh, because you can enlarge the indexing set or refine to a subnet, or similar?
2d
reviewed Close continuous vs discrete random walk
2d
comment Is the module action $M\times M^*\to M^*$ jointly continuous?
A first start would be to see what happens if $M=\ell^\infty$ or $M=L^\infty[0,1]$...
2d
comment Is the module action $M\times M^*\to M^*$ jointly continuous?
Are you sure that for joint continuity it suffices to show that $a_if_i \to af$? I would have expected that one needs to consider something like the product net $(a_if_j)_{i,j\in (I\times J})$ with a suitable ordering. Could you please clarify whether you need joint continuity, or the seemingly weaker requirement that you have stated
2d
comment Number of connected components of a $C^{*}$ algebra
Also, why does an answer for the matrix algebra case tell you what is going on for the finite-dimensional case? It seems perfectly possible that if $A\subset M_n({\bf C})$ then two projections in $A$ could be unitarily equivalent in $M_n({\bf C})$ without being unitarily equivalent in $A$...
2d
comment Number of connected components of a $C^{*}$ algebra
Thanks. So according to your definition, $ncc(M_n({\bf C}))= \log_2(n+1)$? This seems slightly odd, and it's not clear to me why this definition is better than looking at equivalence classes of projections in stabilized versions of the algebra (i.e. $K_0)$.
2d
reviewed Looks OK Reference request for an introduction to deformation theory in algebraic geometry
2d
reviewed Close The Heisenberg uniquness pairs invariants by translation and rotaion?
2d
comment Unitizations of Banach algebras and matrix norms
Surely, before resolving the case of general p, you need to resolve the case p=2?