quotients in $C^{*}$ -algebras

Theorem - Let $\mathcal{A}$ be a $C^{*}$ -algebra (http://planetmath.org/CAlgebra) and $\mathcal{I}\subseteq\mathcal{A}$ a closed (http://planetmath.org/ClosedSet) ideal. Then the involution (http://planetmath.org/InvolutaryRing) in $\mathcal{A}$ induces a well-defined involution in $\mathcal{A}/\mathcal{I}$ and $\mathcal{A}/\mathcal{I}$ is a $C^{*}$ -algebra with this involution and the quotient norm.

Title	quotients in $C^{*}$ -algebras
Canonical name	QuotientsInCalgebras
Date of creation	2013-03-22 17:41:39
Last modified on	2013-03-22 17:41:39
Owner	asteroid (17536)
Last modified by	asteroid (17536)
Numerical id	5
Author	asteroid (17536)
Entry type	Theorem
Classification	msc 46L05
Related topic	NuclearCAlgebra

quotients in C*-algebras

quotients in $C^{*}$ -algebras