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摘要
Let A and B be unital commutative Banach algebras. Suppose that A is semi-simple. Let p: A -> A and tau : B -> B be bijections. If T : A -> B is a surjection with, for some alpha is an element of C/{0}, r(T(f)tau(T(g)) - alpha) = r(fp(g) - alpha) for all f,g is an element of A, then B is semi-simple and r(T(f)T(g)(-1) - 1) = r(fg(-1) - 1) for every f is an element of A and g is an element of A(-1). As a consequence, T(1) is invertible and T(1)(-1)T is a real-algebra isomorphism. If, in addition, T(1)-1-T(i) = i, then T(1)(-1)T is a complex-algebra isomorphism. This result unifies and generalizes [3, Theorem 7.4] and [4, Theorem 3.2 and 6.2].
- 出版日期2011
