Modules with norms which take values in a C*-algebra
Modules with norms which take values in a C*-algebra
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具有以 C* 代数形式取值的范数的模块
DOI：
10.2140/pjm.1998.185.163
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发表时间：
1996
影响因子：
0.6
通讯作者：
N. Weaver
中科院分区：
文献类型：
--
作者：
N. Phillips;N. Weaver
我们考虑C*-代数A上的模E，它具有到A+的映射，该映射具有范数的形式性质。我们完全确定这些模块的结构。特别地，我们证明了，如果A没有非零交换理想，那么每个这样的E必须是一个希尔伯特模。交换的情形则不那么严格：如果A = C 0（X）是交换的，那么E仅仅同构于X上某个Banach空间丛的连续截面模。一般来说，E将嵌入前两种类型的模的直和中。
We consider modules E over a C*-algebra A which are equipped with a map into A+ that has the formal properties of a norm. We completely determine the structure of these modules. In particular, we show that if A has no nonzero commutative ideals then every such E must be a Hilbert module. The commutative case is much less rigid: If A = C0(X) is commutative then E is merely isomorphic to the module of continuous sections of some bundle of Banach spaces over X. In general E will embed in a direct sum of modules of the preceding two types.