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

TL;DR

This paper develops the theory of multipliers for Hilbert pro-$C^{\

Contribution

It introduces the concept of multipliers for Hilbert pro-$C^{\

Findings

Defined the multiplier of a Hilbert pro-$C^{\" ,

Explored the structure of the multiplier bimodule of a Hilbert pro-$C^{\" ,

Analyzed the relationships between crossed products and multiplier algebras in this context.

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-$% C^{\ast }$-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 $A\times _{X}\mathbb{Z}$.