Polynomial identities of Banach algebras (Q515732)

The authors consider PI-algebras \(A\) over the real and complex numbers. An associative algebra \(A\) is said \textit{normed} provided that it has a norm \(\|\cdot \|\) that satisfies \(\| a\cdot b \|\leq \| a \| b\|\) for all \(a,b\in A\). It is a \textit{Banach algebra} if \((A,\|\cdot\|)\) is a complete normed space. It is known that not all PI-algebras are normed algebras. As a main result the authors prove that for a PI-algebra \(A\) there exists a Banach algebra \(B\) that satisfies the same identities.