Is there a Banach algebra which $A^2=\langle a_1a_2 ; a_1,a_2\in A\rangle$ is not dense in $A$ but $(A^{**})^2$ is dense in $A^{**}$?
Is there a Banach algebra which $A^2$ is not dense in $A$ but $(A^{**})^2$ is dense in $A^{**}$?
Mohammad
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