# Journal of Operator Theory

Volume 33, Issue 1, Winter 1995 pp. 3-31.

Modular structure of the crossed product by a compact group dual**Authors**: Tommaso Isola

**Author institution:**Dipartimento di Matematica, Universita di Roma â€œTor Vergataâ€, Via della Ricerca Scientifica, I-00133, Roma, ITALY

**Summary:**Let M be a properly infinite von Neumann algebra, and $\alpha$ a dominant action of a separable compact group. Choose a faithful normal state $\varphi_0$ on the fixed-point algebra $M^\alpha$ and lift it to M as $\varphi \coloneqq \varphi _0 \cdot \varepsilon$ by means of the canonical expectation $\varepsilon {\rm{ : }}M \to M^\alpha$. Then we express the modular objects associated with $\varphi$ in terms of the modular objects associated with $\varphi_0$.

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