Ｖ．Ｐｔáｋ［１］在有单位元的情形下详细研究了Ｂａｎａｃｈ代数．本文将推广他的结果到一般情形．特别，我们引入了可正开拓的正线性泛函，并对它进行了刻划．

V. Pták has given the detailed discussion for a unital Banach * algebra in . In this paper, we will generalize his results to the general case. In particular, we introduce the concept of a positive linear functional with positive extension, and describe its characterizations.