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Results tagged with c-star-algebras
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user 66649
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].
1
vote
Accepted
Integration in C^* algebra
Yes.
$\alpha_s(A)$ is a continuous bounded function.
The function
$f(s) \alpha_s(A)$ is measurable and because of
$$\int_\mathbb{R} \|f(s) \alpha_s(A)\| ds \le \int_\mathbb{R} |f(s)| ds\, \|A\| < \ …
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