Journal of Operator Theory

Volume 48, Issue 2, Fall 2002 pp. 355-367.

Entropy of crossed products and entropy of free products

Authors: Marie Choda
Author institution: Department of Mathematics, Osaka Kyoiku University, Asahigaoka, Kashiwara 582--8582, Japan

Summary: An entropical invariant is defined for automorphisms of countable discrete amenable groups, and relations are shown between two entropies for an automorphism on the $C^*$-crossed product algebra and for its restriction to the original algebra. As an application, given an automorphism $\be$ and an amenable group $G$, we have the equality for entropy that $ht(\underbrace{\be * \cdots * \be} _{|G|}) = ht(\be * \id)$.

Keywords: $C^*$-algebra, entropy, crossed product, reduced free product

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