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Results tagged with oa.operator-algebras
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user 66649
Algebras of operators on Hilbert space, $C^*-$algebras, von Neumann algebras, non-commutative geometry
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Is $KK^G(\mathbb{C}^n,B)$ countably additive in $B$ and countable?
Let $G$ be a finite discrete groupoid, $A=\mathbb{C}^n$ a finite dimensional, commutative $C^*$-algebra and assume we have given a $G$-action on $A$. Note that the action of $G$ on $\mathbb{C}^n=C_0(\ …
- 58
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56
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When is a cycle in $KK^G(A,A)$ with zero operator the identity cycle?
Given a cycle of the form $(\pi,H,0)$ in $KK^G(A,A)$, when is it equivalent to the identity cycle $1_A=(i_A,A,0)$?
The operator $T=0$, and $\pi:A \rightarrow L(H)$ may be injective.
Any criterions h …
- 58
3
votes
1
answer
666
views
K-homology of Cantor set and abelian AF-algebras
This may be a standard question answered in a book, or article. I don't know. I know that there exist related results with $\lim^1$-sequences (Rosenberg and Schochet).
What is
$KK(C_0(X),\mathbb{C}) …
- 58
1
vote
Accepted
Integration in C^* algebra
Yes.
$\alpha_s(A)$ is a continuous bounded function.
The function
$f(s) \alpha_s(A)$ is measurable and because of
$$\int_\mathbb{R} \|f(s) \alpha_s(A)\| ds \le \int_\mathbb{R} |f(s)| ds\, \|A\| < \ …
- 58