Sur la continuité automatique des épimorphismes dans les \(^*\)-algèbres de Banach (Q1774737)

The authors show that every \(*\)-semisimple Banach algebra is semisimple. As a consequence of this property, they conclude that for a \(*\)-semisimple Banach algebra \(B\), every epimorphism from a Banach algebra \(A\) onto \(B\) is continuous, every Banach algebra norm on \(B\) is equivalent to the given norm on \(B\), and the involution \(*\) is continuous.