L~∞-Banach代数的内理想的刻画及同构定理

A CHARACTERIZATION OF INNER IDEAL OF L ∞-Banach ALGEBRAS AND AN ISOMORPHISM THEOREM BETWEEN THEM

首先给出了具有单位元的 Ｌ∞－ Ｂａｎａｃｈ 代数的内理想的刻画，由此推广了［１］ 定理２ ．２ ．然后我们给出了具有收缩逼近单位元的 Ｌ∞ － Ｂａｎａｃｈ 代数之间的一个同构定理．作为推论，我们证明了：两个 Ｃ 代数之间的完全等距映射是同构的．

In this paper, first we gave a characterization of inner ideal of a unital L ∞-Banach algebra A; this result generalized[1] Theorem 2.2. Then we obtain an isomorphism theorem between non-unital L ∞-banach algebras which have contractive approximate identities. As corollary in the last we proved: The completely isometry linear map between two C *-algebras is * isomorphism.