A II$_1$ factor $\mathcal M$ with trace $\tau$ has property Gamma if for every $\epsilon > 0$ and finite set $\{x_1,\cdots, x_n\} \subset \mathcal M$ there exists a trace 0 unitary element $y\in\mathcal M$ such that $\sum_{i=1}^n \|x_iy – yx_i\|_2 < \epsilon$, where the 2-norm is $\|a\|_2 = \tau(a^*a)^{1/2}$. Murray and von Neumann defined this … Read more
For what type of C∗ algebras A, the group of invertible elements of C(S2)⊗A is a connected group? All finite dimensional A satisfy this property. Is it true to say that A satisfy the above property if and only if the group of invertible elements of A is connected? Answer AttributionSource : Link , Question … Read more
I asked this question at math.stackexchange and received no comment. Let A be a C*-algebra and ϕ be a positive linear functional on A. Let ˜ϕ be its unique w∗-continuous extension on A∗∗. Let us put Nϕ:={a∈A:ϕ(a∗a)=0} , N˜ϕ:={x∈A∗∗:ϕ(x∗x)=0} Nϕ forms a closed left ideal in A and N˜ϕ forms a w∗-closed left ideal in A∗∗. It … Read more
The general context for the question – is belief that quantization of compact symplectic manifolds can be endowed with the structure of $C^*$-algebra (see MO230695). The particular question is about the most simple example – sphere $S^2$ with the standard symplectic form. I think that corresponding $C^*$-algebra can be defined explicitly by generators and relations. … Read more
Let H be a non-separable Hilbert space and {ei}i∈I be an orthonormal basis for H. Let J be a uncountable proper subset in I. Let us put E={x∈B(H):‖ One may check that E is an open set in the strong operator topology but not in the weak operator topology. Question1: I feel E is not … Read more
I am trying to understand what (minimal) conditions one would need in order to obtain a functional calculus on a Fréchet algebra, which we demand to be equipped with an involution that leaves all semi-norms invariant. The motivation behind this is that I need to see if forcing a Fréchet algebra to have positive elements … Read more
Closed. This question needs details or clarity. It is not currently accepting answers. Want to improve this question? Add details and clarify the problem by editing this post. Closed 5 years ago. Improve this question I have recently decided on a topic for my master thesis. I want to compare the Baum Connes conjecture as … Read more
This is my first overflow question, so let me apologize in advance if this belongs on http://math.stackexchange.com. Let G be a discrete group. Let λ:G→B(ℓ2(G)) be the left regular representation of G and A(G) the Fourier algebra of G. Given f,g∈A(G), and writing f(s)=⟨λ(s)x,y⟩,g(s)=⟨λ(s)w,z⟩ for some choice x,y,w,z∈ℓ2(G), is there a way to choose (in … Read more
Let A be a unital C∗-algebra and a∈A. If aa∗+1 is invertible in A then the element β(a)=(aa∗+I)−1(aa∗aa∗I) is an idempotent. The formula is similar to the one defining the Bott projection in the classical case. I wanted to know what does the above β mean for the K-theory of A? Does it have any … Read more
Let $n$ be an integer. Andreas Thom mentioned that Camille Jordan showed that there exists some $m \in {\mathbb N}$ (depending on $n$), such that for any pair of $n \times n$-unitaries $u,v \in U(n)$ which generate a finite group, one has $[u^m,v^m] = 1_n$. In particular, there are two distinct words of length $\ell=2m … Read more
