C. Ding wrote a new post, Half exactness of $K_0$ functor, on the site C. Ding's blog 3 weeks, 2 days ago

**Theorem**. Let $require{amscd}$ $begin{CD}

0 @> >> A @>i>> [email protected]>pi>>[email protected]>>>0

end{CD}$ be an exact sequence of $mathbb{C}$-algebras, then

$begin{CD}K_0(A)@>{i_*}>>K_0(B)@>{pi_*}>>K_0(C)end{CD}$

is exact […]C. Ding wrote a new post, elements of $K_0$ group, on the site C. Ding's blog 1 month ago

Let $e$ be an idempotent in a unital algebra $A$ and $u=begin{pmatrix}1-e & e e & 1-eend{pmatrix}$, then $u$ is invertible and $ubegin{pmatrix}1-e & 0 0 & eend{pmatrix}=begin{pmatrix}1 & 0 0 & […]

C. Ding wrote a new post, On Homotopy, on the site C. Ding's blog 1 month, 2 weeks ago

**Lemma**. Suppose $A$ is a unital Banach algebra and $gamma$ is a continuous path in the idempotents of $A$. Then there is a continuous path $u$ in invertible elements of $A$ such that $u(t)gamma(t) […]

C. Ding wrote a new post, Examples of Idempotents, on the site C. Ding's blog 2 months ago

If $e$ is an idempotent in an algebra, so is $ueu^{-1}$ whenever $u$ is invertible.

So, if $e$ and $f$ are homotopic in $M_infty(A)$ if they are homtopic in some $M_n(A)$ where $A$ is a C*-algebra. Note that […]sample wrote a new post, test account information, on the site Sample 2 months, 1 week ago

you can log in to have a full view of this site with the following information:

– **Username**: sample

– **Password**: 12345678sample wrote a new post, Sample Post, on the site Sample 2 months, 1 week ago

## This is a section

This is an inline equation: $x^2=-1$.

This is a centered equation: $$a^2+b^2=c^2.$$

This is a numbered equation: […]

sample wrote a new post, Hello world!, on the site Sample 2 months, 1 week ago

Welcome to [Functors.net](https://functors.net). This is your first post. Enjoy your blogging!

C. Ding's profile was updated 2 months, 2 weeks ago