Two generalizations of the Gleason-Kahane-Z̀elazko theorem
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Two generalizations of the Gleason-Kahane-Z̀elazko theorem. / Christensen, Erik.
In: Pacific Journal of Mathematics, Vol. 177, No. 1, 01.1997, p. 27-32.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Two generalizations of the Gleason-Kahane-Z̀elazko theorem
AU - Christensen, Erik
PY - 1997/1
Y1 - 1997/1
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=0040564726&partnerID=8YFLogxK
U2 - 10.2140/pjm.1997.177.27
DO - 10.2140/pjm.1997.177.27
M3 - Journal article
AN - SCOPUS:0040564726
VL - 177
SP - 27
EP - 32
JO - Pacific Journal of Mathematics
JF - Pacific Journal of Mathematics
SN - 0030-8730
IS - 1
ER -
ID: 384123526