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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 aHilbert pro-$C^{\ast}$-bimodule. We also investigate the relationship betweenthe 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 themultiplier bimodule $M(X)$ of $X$ and the multiplier algebra $M(A\times_{X}\mathbb{Z})$ of $A\times _{X}\mathbb{Z}$.

Multipliers of Hilbert pro-C*-bimodules and crossed products by Hilbert pro-C*-bimodules

Multipliers of Hilbert pro-C-bimodules and crossed products by Hilbert pro-C-bimodules