5
votes
2answers
321 views

Metrics on the space of $C^{*}$ algebras

I think that there is a metric on the huge space of all $C^{*}$ algebras. What is the explicit definition of this metric?may you introduce me a reference? Moreover is the restriction of this ...
7
votes
1answer
190 views

Who first identified the universal $C^*$-algebra generated by an idempotent of norm at most $C$?

So much is known about hermitian and non-hermitian idempotents in a $C^*$-algebra, that someone must have written down the following. Theorem The universal $C^*$-algebra generated by one element ...
2
votes
0answers
77 views

K-Exactness for groups and C*-algebras

We say that a C*-algebra $A$ is K-exact, if for any exact sequence of C*-algebras $0\rightarrow I\rightarrow B\rightarrow B/I\rightarrow0$, the sequences $K_i(I\otimes_{min}A)\rightarrow ...
1
vote
0answers
202 views

Is an exact operator, unitary equivalent to a banded operator?

Let $H$ be an infinite dimensional separable Hilbert space and $B(H)$ the algebra of bounded operators. Definition : Let $(e_{n})_{n \in \mathbb{N}}$ be an orthonormal basis. $T \in B(H)$ is ...
1
vote
0answers
297 views

Hans Saar's thesis

I would love to have a look on some results which are claimed by some people to be in Saar's thesis: H. Saar, Kompakte, vollständig beschränkte Abbildungen mit Werten in einer nuklearen ...
3
votes
1answer
229 views

Amenability at infinity

I have a few questions about amenability at infinity for locally compact, second countable, Hausdorff topological groups. Recall that a locally compact group $G$ is said to be amenable at infinity if ...
9
votes
2answers
285 views

Injectivity of the Baum-Connes assembly map for locally compact groups

Skandalis, Tu and Yu in "The coarse Baum-Connes conjecture and groupoids" proved that: Let $\Gamma$ be a countable group with a proper left-invariant metric $d$. If $\Gamma$ admits a uniform ...
10
votes
2answers
369 views

C*-algebras with no nontrivial endomorphisms

Pick a C*-algebra $A$ and call a (*-)endomorphism $\alpha:A\to A$ nontrivial if it is injective and $\alpha(A)\neq A$. Question: Do there exist infinite dimensional C*-algebras with no nontrivial ...
10
votes
1answer
606 views

Does the hyperfinite II_1 factor admit two irreducible representations that are not unitarily equivalent?

Regarding the hyperfinite $II_{1}$ factor $R$ as $C^{*}$-algebra, is it known whether any two irreducible representations of $R$ are unitarily equivalent? If it is known that there exists a pair of ...
8
votes
1answer
291 views

The Haar state on compact quantum groups $A_u(Q)$ and $A_o(Q)$

Let $Q\in GL_n(\mathbb{C})$. The free unitary quantum group is the universal $C^*$-algebra $A_u(Q)$ with generators $u_{ij},1\leq i,j\leq n$ and relations making $u=(u_{ij})$ as well as ...
6
votes
0answers
348 views

References for “folklore” on strong amenability of (group) C*-algebras?

[Apologies in advance for the prolixity - but I was unsure how much of the story is familiar.] $\newcommand{\ptp}{\widehat{\otimes}} \newcommand{\co}{\operatorname{co}} ...
0
votes
1answer
257 views

The stabilized homotopy category of graded C* algebra

Hi everyone On page 147 of the note "Group C*-Algebras and K-theory" by N.Higson and E.Guentner there are something about the stabilized homotopy category of graded C* algebra, which is a category ...
3
votes
1answer
288 views

Graded $C^*$-algebras can be faithfully represented on a graded Hilbert space

Hi everyone I try to use GNS-construction to show every graded C*-algebras can be faithfully represented on a graded Hilbert space. If $A$ is a graded C*-algebra with grading automorphism $\alpha$ of ...
1
vote
1answer
620 views

Strict positivity in dense subalgebras of $C^{*}$-algebras

Let $A$ be a $C^{*}$-algebra, represented on a Hilbert space $H$, and $D$ a selfadjoint unbounded operator on $H$ (note that we do not impose that $D$ have compact resolvent). Let ...
12
votes
4answers
2k views

Reference: Learning noncommutative geometry and C^* algebras

I am starting to study noncommutative geometry and C^* algebras so my question is Does anyone knows a good reference on this subject? I would like a basic book with intuitions for definitions and ...
2
votes
1answer
545 views

Reference needed for: every idempotent in a C*-algebra is similar to a hermitian one

The result stated in the title is thoroughly standard - or that's the impression I got. I seem to remember seeing it stated somewhere in a book I was reading in the library, and then ...