A Characterization of Ideals of C* -Algebras
AbstractLet 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.
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2018 ◽
Vol 17
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pp. 1850169
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2012 ◽
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pp. 1021-1046
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1966 ◽
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