All Questions
7 questions
3
votes
1
answer
190
views
A possible spectral characterization of commutative $C^*$ algebras
Let $A$ be a $C^*$ algebra. Assume that
the spectrum $Sp(a_1a_2\ldots a_{n-1}a_n)$ is unchanged as a set after a permutation of $a_i$'s. (unless possible emerge or removing 0 from the spectrum)
Does ...
- 356
2
votes
0
answers
90
views
The group of quasi unitary elements of a (simple) Banach algebra
For a Banach algebra $A$ with invertible group $G(A)$ we define the following group:
$$QG(A)=\{u\in G(A)\mid \;\text{the mapping}\; a\mapsto u^{-1} a u \;\text{is an isometry}\}$$
What is an ...
- 356
3
votes
0
answers
185
views
Non commutative Teichmuller theory
Perhaps the first example in Teichmuller theory is the following proposition:
Proposition: Let $1<r<R$. Then two annular region $U_r=\{z\in \mathbb{C}\bigm|1<|z|<r\}$ and $U_R=\{z\in \...
- 356
4
votes
2
answers
254
views
$K$-theory and surjective norm-decreasing $*$-homomorphisms between $C^*$-algebras
Let $A$ and $B$ be two $C^*$-algebras, and let $p:A \to B$ be a surjective norm-decreasing $*$-homomorphism which is injective on a dense $*$-sub-algebra of $A$. Can such a map have non-trivial kernel,...
- 969
4
votes
1
answer
362
views
$K$-Theory of finite dimensional Banach algebras
Is there a finite dimensional Banach algebra $A$ for which $K_{0}(A)$ is a finite group?
I asked this question in MSE but I received no answer
https://math.stackexchange.com/questions/1624250/...
- 356
2
votes
1
answer
357
views
Non commutative topological manifolds
Assume that $A$ is a Banach algebra with two closed two sided ideals $I$ and $J$ such that $I$ and $J$ are commutative and $A=I+J$. Does this implies that $A$ is commutative? For the $C^{*...
- 356
5
votes
1
answer
342
views
NonCommutative Baire theorem
The classical Baire theorem says that the intersection of a sequence of open dense subsets of $X$, is dense, if the space is compact Hausdorff. In the language of $C^{*}$ algebras this is ...
- 356