标题： Hilbert C*-模的乘子模块再探讨 显示英文标题

标题： Multiplier modules of Hilbert C*-modules revisited

摘要： Hilbert C*-模的乘子模理论被重新考虑，以获得这些特殊Hilbert C*-模的更多性质。 一个Hilbert C*-模成为乘子C*-模的性质被证明在强Morita等价理论中作为C*-对应关系的左或右Hilbert C*-模时是一个不变量。 对于Hilbert C*-模及其相应的乘子模对，''紧''算子的C*-代数、有界模算子的巴拿赫代数以及到其C*-对偶巴拿赫C*-模的有界模算子的巴拿赫空间之间的相互关系被表征。 后者上的结构总是等距嵌入到前者相应的结构中。 给出了从初始Hilbert C*-模到其乘子模的这些类型的有界模算子延续失败的例子，然而存在的延续被证明总是唯一的。 同样地，比较了来自两种类型的Hilbert C*-模到其相应系数C*-代数的有界模泛函，并最终证明存在的延续是唯一的。 显示英文摘要

摘要： The theory of multiplier modules of Hilbert C*-modules is reconsidered to obtain more properties of these special Hilbert C*-modules. The property of a Hilbert C*-module to be a multiplier C*-module is shown to be an invariant with respect to the consideration as a left or right Hilbert C*-module in the sense of a C*-correspondence in strong Morita equivalence theory. The interrelation of the C*-algebras of ''compact'' operators, the Banach algebras of bounded module operators and the Banach spaces of bounded module operators of a Hilbert C*-module to its C*-dual Banach C*-module are characterized for pairs of Hilbert C*-modules and their respective multiplier modules. The structures on the latter are always isometrically embedded into the respective structures on the former. Examples for which continuation of these kinds of bounded module operators from the initial Hilbert C*-module to its multiplier module fails are given, however existing continuations turn out to be always unique. Similarly, bounded modular functionals from both kinds of Hilbert C*-modules to their respective C*-algebras of coefficients are compared, and eventually existing continuations are shown to be unique.