摘要
设A是一个复交换Banach代数.本文在G·Corach等人给出的“可约”概念基础上,证明了A中可约元(α,α)的几个有趣的等价条件.主要结果是:若A是一个复交换Banach代数,(α,α)∈U_(n+1)(A).则(α,α)在A中可约的充分必要条件是存在f_m∈U_n(C(σ(A))),使得‖f_m-α‖Zα→0.这里‖f_m‖Zα=sup{‖f_m(h)h∈Z_α}.(m∈N).
On the basis of the concept of reducibility, this paper proves some equivalent conditions for a reducible element(α,α)∈U_(n+1)(A), The result is that if A is a complex commutative Banach algebra,(α,α)∈U_(n+1)(A), then(α,α) be reducible in A if and only if there exists f_m∈U_n(C(σ(A))),such that‖f_m-α‖→0, where‖f_m‖Zα=sup{‖f_m(h)‖|h∈Zα}(m∈N).
