On a certain 𝐶*-crossed product inside a 𝑊*-crossed product

Olesen, Dorte; Pedersen, Gert K.

doi:10.1090/S0002-9939-1980-0572308-8

On a certain $C^{\ast }$-crossed product inside a $W^{\ast }$-crossed product
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by Dorte Olesen and Gert K. Pedersen

Proc. Amer. Math. Soc. 79 (1980), 587-590

DOI: https://doi.org/10.1090/S0002-9939-1980-0572308-8

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Abstract:

To each ${W^ \ast }$-dynamical system $(\mathfrak {M},G,\alpha )$ corresponds canonically a ${C^ \ast }$-dynamical system $({\mathfrak {M}^c},G,\alpha |{\mathfrak {M}^c})$. We show that the ${C^ \ast }$-crossed product $G{ \times _\alpha }{\mathfrak {M}^c}$ can be identified with a certain ${C^ \ast }$-subalgebra of the ${W^ \ast }$-crossed product $G{ \times _\alpha }\mathfrak {M}$.

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