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A Characterization of Ideals of C* -Algebras

Published online by Cambridge University Press:  20 November 2018

Masaharu Kusuda
Masaharu Kusuda*
Affiliation:
Department of Applied Mathematics Faculty of Engineering Science Osaka University Toyonaka, Osaka 560 Japan.
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Abstract

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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.

Keywords

46L3046L05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 4 , 01 December 1990 , pp. 455 - 459
Copyright
Copyright © Canadian Mathematical Society 1990

References

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