Doplicher, Sergio; Roberts, John E. Compact group actions on \(C^*\)-algebras. (English) Zbl 0689.46020 J. Oper. Theory 19, No. 2, 283-305 (1988). This work is a contribution to the formulation of an abstract duality theory for compact groups into the framework of \(C^*\)-algebras. More specifically it treats certains aspects of the spectral analysis of the actions \(\alpha\) of compact groups G on infinite \(C^*\)-algebras B by looking at \(\alpha\)-stable Hilbert spaces H in B. Some variants of the Tannaka-Krein theorem are proved in this context, given conditions for a compact group G to agree with the stabilizer in Aut B of the fixed point algebra. A Galois correspondence between some subalgebras of B and normal subgroups of G is constructed, and the structure of the relative commutant is studied. The paper ends with the construction of examples illustrating the setting of this work. Reviewer: G.Loupias Cited in 1 ReviewCited in 10 Documents MSC: 46L55 Noncommutative dynamical systems Keywords:abstract duality theory for compact groups; framework of \(C^*\)- algebras; Tannaka-Krein theorem; stabilizer; fixed point algebra; Galois correspondence PDFBibTeX XMLCite \textit{S. Doplicher} and \textit{J. E. Roberts}, J. Oper. Theory 19, No. 2, 283--305 (1988; Zbl 0689.46020)