Two Generalizations of the Gleason-kahane-z̀elazko Theorem
نویسنده
چکیده
In this article we obtain 2 generalizations of the well known Gleason-Kahane-Z̀elazko Theorem. We consider a unital Banach algebra A, and a continuous unital linear mapping φ of A into Mn(C) – the n × n matrices over C. The first generalization states that if φ sends invertible elements to invertible elements, then the kernel of φ is contained in a proper two sided closed ideal of finite codimension. The second result characterizes this property for φ in saying that φ(Ainv) is contained in GLn(C) if and only if for each a in A and each natural number k: trace(φ(a)) = trace(φ(a)) .
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