bio  website  www2.unine.ch/alain.valette 

location  Neuchâtel, Switzerland  
age  56  
visits  member for  4 years 
seen  3 hours ago  
stats  profile views  4,841 
3h

answered  Irreducible representation of $C^*(D_\infty)$, group $C^*$algebra of an infinite dihedral group 
9h

comment 
Using $\mathcal{U(H)}$ as a model for $EG$ and working with the Fredholm Operators
The universal representation $(U_t)$ of the real line is not norm continuous (reason: $\U_t1\=2$ for $t\neq 0$). This should discourage you to use the norm topology on $U(\mathcal{H})$ for your problem. 
Apr 21 
comment 
Determining the primitive ideal space of Cstar algebras
The example you consider is very special, as it is the $C^*$algebra of the infinite dihedral group, which is notoriously type I. The spectrum in that case is "an interval with 2+2 endpoints", i.e. the union of two closed intervals identified along their interiors. This wellknown fact can be found e.g. in these notes by I. Putnam: math.uvic.ca/faculty/putnam/t/Math_533_Lecture_Notes.pdf 
Apr 21 
revised 
“Relative cone types” for groups relative to some collection of subgroups
Fixed spelling 
Apr 18 
awarded  Yearling 
Apr 16 
comment 
Using $\mathcal{U(H)}$ as a model for $EG$ and working with the Fredholm Operators
What are the assumptions on $G$, exactly? And what do you mean by "a/the unitary universe"? Is it the universal representation (so that $G$ is secretly locally compact)? 
Mar 19 
revised 
Recollement of multiple $t$structures
Spelling fixed in title 
Mar 13 
awarded  Enlightened 
Mar 9 
comment 
Product of two foliations
Am I missing something? For question 2, isn't it clear from the definitions that $C^*(F\times F')=C^*(F)\otimes C^*(F')$ (minimal tensor product)?. Think that, if the leaf spaces are Hausdorff, then $C^*(F)$ is Morita equivalent to $C_0(M/F)$, so $C^*(F\times F')$ is Morita equivalent to $C_0((M\times N)/(F\times F'))=C_0(M/F)\otimes C_0(N/F')$. 
Feb 7 
awarded  Necromancer 
Jan 19 
comment 
The kernel of $C^{*}(G)\to C_{r}^{*}(G)$
See "On Isolated Points in the Dual Spaces of Locally Compact Groups", by S. P. Wang, Mathematische Annalen (1975) Volume: 218, page 1934; available on gdz.sub.unigoettingen.de/dms/load/img/… 
Jan 17 
comment 
The kernel of $C^{*}(G)\to C_{r}^{*}(G)$
This is a wide open question. I personally believe that, for $G$ discrete, the question is intractable, because a description of $I(G)$ is very much related to a description of the dual $\hat{G}$. As an example, consider a residually finite group with property (T). It is known that each finitedimensional rep is isolated in $\hat{G}$, so defines a direct summand of $C^*(G)$ isomorphic to a matrix algebra. So $I(G)$ contains a huge direct sum of matrix algebras, and probably lots of other stuff too. 
Jan 15 
comment 
Embedding Euclidean buildings into products of trees
You're right, I overlooked the surjectivity issue. I leave my comment however, as a very partial contribution. 
Jan 15 
awarded  Nice Answer 
Jan 14 
comment 
Embedding Euclidean buildings into products of trees
I think taking $p=1$ is prevented by the KleinerLeeb result on quasiisometric rigidity of Euclidean buildings: see Theorem 1.1.2 in math.nyu.edu/~bkleiner/symm.pdf 
Jan 7 
awarded  Enlightened 
Jan 7 
awarded  Nice Answer 
Jan 7 
answered  Can the full and reduced group $C^*$algebras be “noncanonically” isomorphic? 
Jan 5 
comment 
Are normcontinuous representations smooth?
The 2nd proof is obviously correct, and actually shows that there is a commutative diagram linking $d\rho:\mathfrak{g}\rightarrow A$ and $\rho:G\rightarrow A^{inv}$, where the vertical arrows are given by the exponential maps of $G$ and $A$ respectively. 
Jan 5 
comment 
MathScinet reviewing: should I check the proofs?
I think we all agree that, as a reviewer for MR, you're not supposed to check the proofs. Trouble may arise if you find a mathematical mistake in the paper, because you are supposed to explain why it is false, or provide a counterexample, and this can result in painfully long and not so informative reviews. 