| In this talk, we study real Banach * algebras systematically, such as complexification, abelian case, * representation (GNS construction), * radical, enveloping real C*-algebra, symmetricity. In particular, we present the right from of Ptak's inequality in the real case, and generalize Vukman's results. Indeed, this work is a real analogue of Ptak's work in the complex case. |