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A C*-algebra is a complex Banach algebra together with an isometric antilinear involution satisfying (a b)* = b* a* and the C*-identity ‖a* a‖ = ‖a‖². Related tags: [banach-algebras], [von-neumann-algebras], [operator-algebras], [spectral-theory].
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Why is this a conditional expectation into the fixed point algebra?
Let $G$ be a compact group with Haar measure $\mu$ normalised such that $\mu (G)=1$. Let $A$ be a C*-algebra and $\alpha : G\rightarrow \text{Aut} (A)$ a continuous action of $G$ on $A$. Define
$$
E(x …