All Questions
Tagged with noncommutative-geometry banach-algebras
14 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
2
votes
1
answer
151
views
Automorphism of algebras with certain initial conditions on given idempotents
The First question
Let $A$ be a Banach or a $C^*$ algebra. Assume that $e,f$ are two idempotents or prjections in $A$ which satisfy $ef=fe=0$. Assume that there are two automorphisms $\phi, \psi: A \...
- 356
4
votes
0
answers
333
views
Other kinds of equivalence relations on the set of idempotents of a Banach or $C^*$-algebra or a ring (Can we get a new kind of K-theory?)
The standard equivalent relations on idempotents of a $C^*$ algebra or a Banach algebra are Murray von Neumann, similarity and homotopy equivalent. In this post we consider two other kinds of ...
- 356
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
7
votes
1
answer
391
views
Can a finite von Neumann algebra be strongly morita equivalent to a properly infinite von neumann algebra?
Can a finite (by finite I mean when the projection $1$ is finite) von Neumann algebra be strongly morita equivalent to a properly infinite von Neumann algebra?
(Strong morita equivalence is the same ...
- 360
5
votes
0
answers
300
views
Can we obtain a derived category from an additive category? Like a category of Banach modules?
Let $A$ be a Banach algebra, let $A$-mod be the category of left Banach modules (as defined in Helemskii's "Banach and locally convex algebras"), $A$-mod is an additive category, but not abelian ...
- 211
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
0
votes
3
answers
364
views
Specific Reference? Noncommutative topology and C^* algebras [closed]
I stumbled across this "dictionary for noncommutative topology" http://planetmath.org/noncommutativetopology
and I would be very interested in learning more on the subject, particularly I'd like to ...
- 11
2
votes
1
answer
187
views
Unitization via "End points compactification"
We know that every compactification of locally compact Hausdorff spaces correspond to a unitization of $C^{*}$ algebras. For example the one point compactification corresponds to the minimal ...
- 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
0
votes
0
answers
208
views
A noncommutative analogy of the tube lemma
Assume that $A$ and $B$ are two unital commutative Banach algebras. Assume that $\phi \in \mathcal{M} (A)$ is an element of the maximal Ideal space. Define $\alpha: A\hat{\otimes} B \to \mathbb{C}\...
- 356