866 reputation
520
bio website
location Germany
age 26
visits member for 3 years, 10 months
seen Dec 16 at 7:26

Dec
8
awarded  Caucus
Dec
6
accepted Cap product between K-Theory and K-Homology
Dec
5
comment Cap product between K-Theory and K-Homology
@QiaochuYuan: Oh, yes, you are right ... $aT$ is an element of $\mathfrak{D}(A)$ in general only if $A$ is commutative. I completely forgot to check this, because I was somehow fixed only on checking if the map is a $^\ast$-homomorphism. Thank you! You can post it as an answer so that I can accept it.
Dec
5
comment Cap product between K-Theory and K-Homology
@NajibIdrissi: why did you delete the $K$-homology tag?
Dec
5
comment Cap product between K-Theory and K-Homology
Given a representation $\rho\colon A \to \mathbb{B}(H)$ of the $C^\ast$-algebra $A$ on a separable Hilbert space $H$, one defines the dual algebra $\mathfrak{D}(A)$ of $A$ as $\mathfrak{D}(A) := \{ T \in \mathbb{B}(H) \colon [T,\rho(a)] \in \mathfrak{K} \text{ for all }a \in A\}$. Here $\mathfrak{K}$ are the compact operators. The $K$-homology of $A$ is then defined as $K^p(A) := K_{1-p}(\mathfrak{D}(A^+))$, where $A^+$ is the unitization of $A$ and we use an ample representation to form the dual algebra.
Oct
22
awarded  Popular Question
Jul
2
awarded  Curious
Jun
12
answered K-theory computation for algebra of bounded continuous functions on $[0,\infty)$
Jun
12
answered Roe algebra of a countably infinite set of points
Apr
28
accepted Does completing a normed space commute with taking quotients?
Apr
27
comment Does completing a normed space commute with taking quotients?
Thanks! One remaining question: why is the map $\overline{X / Y} \to \overline{X} / \overline{Y}$ surjective?
Apr
27
asked Does completing a normed space commute with taking quotients?
Apr
24
awarded  Citizen Patrol
Apr
12
awarded  Custodian
Apr
12
revised Index of summation shift
improved formatting
Apr
12
reviewed Reviewed Index of summation shift
Apr
12
suggested approved edit on Index of summation shift
Feb
15
awarded  Yearling
Feb
3
comment When do weak and original topology coincide?
Posted my question at MO so that any possible answer does not get lost in the comments: mathoverflow.net/q/156538/13356
Jan
31
reviewed Reviewed Distance from curve to plane