Two generalizations of the Gleason-Kahane-Z̀elazko theorem
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In this article we obtain 2 generalizations of the well known Gleason-Kahane-Zelazko Theorem. We consider a unital Banach algebra 21, and a continuous unital linear mapping φ of 21 into Mn(ℂ) - the n x 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(21inv) is contained in GLn(ℂ) if and only if for each o in 21 and each natural number k: trace(φ(ak)) = trace(φ(a)k).
Original language | English |
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Journal | Pacific Journal of Mathematics |
Volume | 177 |
Issue number | 1 |
Pages (from-to) | 27-32 |
Number of pages | 6 |
ISSN | 0030-8730 |
DOIs | |
Publication status | Published - Jan 1997 |
ID: 384123526