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edited Jul 5, 2021 at 19:21

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fa.functional-analysis ac.commutative-algebra oa.operator-algebras

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asked Jul 5, 2021 at 15:43

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Is there a Banach algebra which $A^2$ is not dense in $A$ but $(A^{})^2$ is dense in $A^{}$?

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 $A^{**}$?

ac.commutative-algebra oa.operator-algebras