Hi,

This is the next problem in that theme. How can I show the following:

If we take natural embedding

$\displaystyle T:A_1 \rightarrow A_1 \oplus A_1$

then it satisfy $\displaystyle Txy=TxTy$ but neither

$\displaystyle \sigma(Tx) \in \sigma(x)$

nor

$\displaystyle Te_1=e_2$

However we have $\displaystyle \sigma(x) \in \sigma(Tx)$.

Thanks for any help.