Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

An element $x$ in the $C^*$-algebra $A$ is well-supported if there is a $p\in A$ with $x=xp$ and $x^*x$ invertible in $pAp$.

That is the definition, but I cannot catch the key of it. Maybe you can show me some examples, which one is well-supported, which one is not, and what is the motivation.

share|cite|improve this question
Is $p$ a projection? Where did you encouter this definition? – Rasmus Sep 27 '11 at 11:02
Yes,a projection p∈A,I am sorry I forget it. – Strongart Sep 29 '11 at 10:20
Could you give some context? Where did you encouter this definition? – Rasmus Sep 29 '11 at 13:53
In the special case where $A=B(H)$, you can show that $p$ is the orthogonal projection onto $\ker(x)^\perp$, and $x$ is well-supported if and only if $x|_{\ker(x)^\perp}$ is bounded below. – Jonas Meyer Jul 3 '12 at 6:43

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.