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- W1553202469 abstract "We introduce the notion of the crossed product $A rtimes _Xmathbb {Z}$ of a $C^*$-algebra $A$ by a Hilbert $C^*$-bimodule $X$. It is shown that given a $C^*$-algebra $B$ which carries a semi-saturated action of the circle group (in the sense that $B$ is generated by the spectral subspaces $B_0$ and $B_1$), then $B$ is isomorphic to the crossed product $B_0 rtimes _{B_1}mathbb {Z}$. We then present our main result, in which we show that the crossed products $A rtimes _Xmathbb {Z}$ and $B rtimes _Ymathbb {Z}$ are strongly Morita equivalent to each other, provided that $A$ and $B$ are strongly Morita equivalent under an imprimitivity bimodule $M$ satisfying $Xotimes _A M simeq Motimes _B Y$ as $A-B$ Hilbert $C^*$-bimodules. We also present a six-term exact sequence for $K$-groups of crossed products by Hilbert $C^*$-bimodules." @default.
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- W1553202469 date "1998-01-01" @default.
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- W1553202469 title "Morita equivalence for crossed products by Hilbert $C^ast $-bimodules" @default.
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- W1553202469 doi "https://doi.org/10.1090/s0002-9947-98-02133-3" @default.
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