Geodesic
A Characterization of Ideals of C* -Algebras
Canadian mathematical bulletin, Tome 33 (1990) no. 4, pp. 455-459

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Let A be a C*-algebra and let I be a C*-subalgebra of A. Denote by an extension of a state φ of B to a state of A. It is shown that I is an ideal of A if and only if there exists a homomorphism Q from A** onto I** such that Q is the identity map on I** and for every state φ on I. Furthermore it is also shown that I is an essential ideal of A if and only if there exists an injective homomorphism from A into the multiplier algebra of I which is the identity map on I.
DOI : 10.4153/CMB-1990-074-4
Mots-clés : 46L30, 46L05 
Kusuda, Masaharu. A Characterization of Ideals of C* -Algebras. Canadian mathematical bulletin, Tome 33 (1990) no. 4, pp. 455-459. doi: 10.4153/CMB-1990-074-4
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     author = {Kusuda, Masaharu},
     title = {A {Characterization} of {Ideals} of {C*} {-Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {455--459},
     year = {1990},
     volume = {33},
     number = {4},
     doi = {10.4153/CMB-1990-074-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-074-4/}
}
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