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let

Let $A$ ba a Banach algebra and $u$ be an arbitrary free ultrafilter. let Let $A^{#}$ A^{\bullet}$ be the unitization of $A$. can Can we have ${(A)_u}^{#}=(A^{#})_u$???????????((A)_{u})^{\bullet} = (A^{\bullet})_{u}$?

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ultrapowers of Banach algebras

let $A$ ba a Banach algebra and $u$ be an arbitrary free ultrafilter. let $A^{#}$ be the unitization of $A$. can we have ${(A)_u}^{#}=(A^{#})_u$???????????