Multipliers of Hilbert pro-C-bimodules and crossed products by Hilbert pro-C-bimodules
In this paper we introduce the notion of multiplier of a Hilbert pro-$C^{\ast }$-bimodule and we investigate the structure of the multiplier bimodule of a Hilbert pro-$C^{\ast}$-bimodule. We also investigate the relationship between the crossed product $A\times _{X}\mathbb{Z}$ of a pro-$% C^{\ast }$...
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Zusammenfassung: | In this paper we introduce the notion of multiplier of a Hilbert pro-$C^{\ast
}$-bimodule and we investigate the structure of the multiplier bimodule of a
Hilbert pro-$C^{\ast}$-bimodule. We also investigate the relationship between
the crossed product $A\times _{X}\mathbb{Z}$ of a pro-$% C^{\ast }$-algebra $A$
by a Hilbert pro-$C^{\ast }$-bimodule $X$ over $A$, the crossed product
$M(A)\times _{M(X)}\mathbb{Z}$ of the multiplier algebra $M(A)$ of $A$ by the
multiplier bimodule $M(X)$ of $X$ and the multiplier algebra $M(A\times
_{X}\mathbb{Z})$ of $A\times _{X}\mathbb{Z}$. |
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DOI: | 10.48550/arxiv.1412.2270 |