My question is concerned with the involution in Banach \*-algebras. 


**1- Should the involution be assumed continuous in every Banach \*-algebra?** 


If the answer is negative, 


**2- Does there exist any characterization of Banach \*-algebras whose involution is continuous (isometry)?!**



Continuity of the involution in Banach *-algebras
For 1), this is § 36 (pp. 190) of Bonsall & Duncan: The following are equivalent for a Banach \*-algebra $A$, and the set $\text{Sym}(A')$ of all continuous self-adjoint linear functionals on $A$


* The linear involution $f \mapsto f^\*$ is continuous on $A$
* $\text{Sym}(A')$ is separating on $A$
* $\text{Sym}(A)$ is closed on $A$


