Youssef Tdli, Automatic Continuity for Banach Algebras with Involution, Journal of Modern Mathematics and Statistics, Volume 14,Issue 2, 2020, Pages 27-30, ISSN 1994-5388, jmmstat.2020.27.30, (https://makhillpublications.co/view-article.php?doi=jmmstat.2020.27.30) Abstract: Conditions are given for a Banach algebra A with involution which insure that every derivation on A is continuous. To do this, we define and study on a concept called *-semi-simplicity. Keywords: separating ideal;automatic continuity;*-semi-simple algebra;*-simple algebra;*-Algebra