Evaluate $\operatorname{Rad}(A/\operatorname{Rad}(A))$ in a Banach algebra

Asked Oct 26 '18 at 16:12

Active Oct 26 '18 at 19:56

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I've asked this question here

Let $A$ be a Banach algebra with identity $e_A$, I'd like to find

$\operatorname{Rad}(A/\operatorname{Rad}(A)).$

whre we define

$\operatorname{Rad}(A)=\{a\in A:e_A-ba \in \text{InvA},b\in A\}$

I think it's equal $\operatorname{Rad}(A)$

but I didn't get any hint how to prove that, please let me know how to prove that

Any piece of advice would be much appreciated.

edited Oct 26 '18 at 19:56

asked Oct 26 '18 at 16:12

user62498

Your link seems to be to a different question; and this question belongs better on MSE anyway. – Yemon Choi Oct 26 '18 at 17:06
1

Have you considered the case where Rad(A) has codimension 1 in A? – Yemon Choi Oct 26 '18 at 17:07
@Dear Yemon Choi , you are right I correct it – user62498 Oct 26 '18 at 19:57

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