Journal of Operator Theory

Volume 64, Issue 1, Summer 2010 pp. 19-34.

Takai duality for crossed products by Hilbert *-bimodules

Authors: Beatriz Abadie
Author institution: Centro de Matematica, Facultad de Ciencias, Igua 4225, CP 11 400, Montevideo, Uruguay

Summary: We discuss the crossed product by the dual action $\delta$ of the circle on the crossed product $\acx$ of a \cstar-algebra $A$ by a Hilbert \cstar-bimodule $X$. When $X$ is an $A$-$A$ Morita equivalence bimodule, the double crossed product $A\rtimes X\rtimes_\delta S^1$ is shown to be Morita equivalent to the \cstar-algebra $A$.

Keywords: Takai duality, crossed products by Hilbert $C^*$-bimodule

Contents Full-Text PDF