Two generalizations of the Gleason-Kahane-Z̀elazko theorem

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Two generalizations of the Gleason-Kahane-Z̀elazko theorem. / Christensen, Erik.

I: Pacific Journal of Mathematics, Bind 177, Nr. 1, 01.1997, s. 27-32.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Christensen, E 1997, 'Two generalizations of the Gleason-Kahane-Z̀elazko theorem', Pacific Journal of Mathematics, bind 177, nr. 1, s. 27-32. https://doi.org/10.2140/pjm.1997.177.27

APA

Christensen, E. (1997). Two generalizations of the Gleason-Kahane-Z̀elazko theorem. Pacific Journal of Mathematics, 177(1), 27-32. https://doi.org/10.2140/pjm.1997.177.27

Vancouver

Christensen E. Two generalizations of the Gleason-Kahane-Z̀elazko theorem. Pacific Journal of Mathematics. 1997 jan.;177(1):27-32. https://doi.org/10.2140/pjm.1997.177.27

Author

Christensen, Erik. / Two generalizations of the Gleason-Kahane-Z̀elazko theorem. I: Pacific Journal of Mathematics. 1997 ; Bind 177, Nr. 1. s. 27-32.

Bibtex

@article{d6bc4742d4fd450faeada18f19d34f69,
title = "Two generalizations of the Gleason-Kahane-{\`Z}elazko theorem",
abstract = "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).",
author = "Erik Christensen",
year = "1997",
month = jan,
doi = "10.2140/pjm.1997.177.27",
language = "English",
volume = "177",
pages = "27--32",
journal = "Pacific Journal of Mathematics",
issn = "0030-8730",
publisher = "Mathematical Sciences Publishers",
number = "1",

}

RIS

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