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

Abstract

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--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 $A{\times }_X\mathbb{Z}$.

To appear in Operators and Matrices. arXiv admin note: text overlap with arXiv:1410.7823