All Questions
Tagged with c-star-algebras oa.operator-algebras
66 questions
3
votes
1
answer
274
views
Finite codimensional subvector space of $C^{*}$ algebras which contains no invertible elements
Assume that $A$ is a unital $C^{*}$ algebra. Is there a subvector space $Y\subset A$ of finite codimension which does not contain any invertible element?
Let $n(A)$ be the infimum of such ...
- 356
3
votes
2
answers
397
views
Is the ideal property of $X^{**}$ inheritable to $X$?
Let $X$ be an operator space such that there is a weak$^*$-continuous complete isometry $\phi$ from its second dual $X^{**}$ into a $W^*$-algebra $M$ in which $\phi(X^{**})$ is a (necessarily weak$^*$-...
- 619
3
votes
1
answer
161
views
Simple $Z^{*}$ algebra
What is an example of a simple $C^{*}$ algebra which all elements are (two sided or equivalently one sided) zero divisor?
- 356
2
votes
1
answer
131
views
Closeness of points in the irreducible decomposition of a C$^{*}$-algebra representation
Suppose $X$ and $Y$ are compact metric spaces. Let $\varphi\colon C(X)\to M_{n}(C(Y))$ be any $*$-homomorphism. If $\pi$ is an irreducible representation of $M_{n}(C(Y))$, then $\pi$ is unitarily ...
- 267
2
votes
2
answers
190
views
Results which are known about ideals of spatial tensor product
I am studying about ideals of spatial (minimal) tensor product of $C^{\ast}$-algebras but I did not find any book/paper in which all the results are given.
What are some results or folklore which ...
- 1,115
2
votes
1
answer
352
views
K-Theory of $C^{*}(X)$
I'm new to K-Theory for $C^{*}$-algebra and $C^{*}$-algebra of groups.
If $X$ is the group of finite support bijections of natural numbers then what is the K-Theory of $C^{*}(X)$?
I was planning to ...
- 581
2
votes
1
answer
368
views
On diagonal part of tensor product of $C^*$-algebras
Suppose we have a $C^*$-algebra $\mathcal{U}$, Consider the $C^*$-subalgebra generated by elements of the form $a\otimes a$, what is it isomorphic to? Is it isomorphic to $\mathcal{U}$ itself?
- 677
2
votes
1
answer
244
views
$R$ is a right multiplier and $R(a)b=a\overset{?}{\implies} A$ is unital
Let $A$ be a $C^*$-algebra, and $R:A\to A$ its right multilplier. Is it true that
$$
\exists b\in A\quad \forall a\in A \quad R(a)b=a\qquad
$$
implies $A$ is unital. I know this is true if A is a weak$...
- 1,697
2
votes
0
answers
208
views
A functor on the category of rings, algebras or compact Hausdorff topological space
Assume that $R$ is a unital ring or a complex or real (Banach or $C^{*}$) algebra.
We define a relation $M$ on $R$ as follows: $$a\;M b \;\;\; \text{iff}\;\; a=xy,\;b=yx \;\; \text{for ...
- 356
1
vote
1
answer
306
views
Simple $C^*$ algebras whose all commutator elements have scalar square
Is there a simple $C^*$ algebra $A$, not isomorphic to $M_2(\mathbb{C})$, such that for every commutator element $x=ab-ba$, $x^2$ is an scalar element?
- 356
1
vote
0
answers
356
views
Determining the primitive ideal space of C-star algebras
Is there a general way of finding a primitive ideal space of $C^*$-algebra?
For example, if $C^*$-algebra is given by the universal $C^*$-algebra generated by two self-adjoint unitary elements, how ...
- 11
1
vote
0
answers
182
views
Characterization of exact groups via the existence of amenable actions on unital C*-algebras
It is known that a discrete group $G$ is exact if and only if it admits an amenable action on a compact topological space. Would it also be true that $G$ is necessarily exact when it admits an ...
- 2,263
1
vote
0
answers
164
views
When a finite codimensional subalgebra contains a finite codimension ideal?
What is a classification of all algebras $A$ (purely algebraic algebras, Banach or $C^*$ algebras or Lie algebras) with the following property:
Every finite codimensional subalgebra $B$ of $A$ ...
- 356
1
vote
0
answers
178
views
A locally convex $C^*$ algebra without zero divisor
Let we have a locally convex $C^*$ algebra $A$. That is $A$ is a TVS equipped with an algebra and an involution structure such that all operations are continuous. Moreover the topology on $A$ ...
- 356
1
vote
0
answers
81
views
A consecutive resolution of continum algebras to a simple continum algebra
Motivated by classical Gelfand Naimark duality, the correspondence between the category of commutative $C^{*}$ algebras and the category of locally compact Hausdorff spaces, we ...
- 356
0
votes
1
answer
124
views
Definition of center of ternary ring of operators
Let $H$ and $K$ be Hilbert spaces and $B(H,K)$ denotes the space of bounded operators from $H$ to $K$. Recall that a ternary ring of operators (TRO) $V$ is a closed subspace of $B(H,K)$ which is ...
- 1,115