The aim of this work is to study norm preserving extensions of completely positive and completely contractive maps on some spaces of fractions with values in a space of sesquilinear forms on a inner product space. The main result is stated in the case of non necessarily commutative C*-algebras with unit. Moreover, the main result is applied to characterize a “quaternionic” version of the operator moment problem. for this application, a special measure is introduced.

中文翻译：

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完全正性和四元数矩问题

这项工作的目的是研究分数阶的某些空间上完全正和完全收缩的映射的范数保持扩展，其内积空间上的倍数形式空间中的值。在具有单位的非必然交换C *-代数的情况下，陈述了主要结果。此外，主要结果被应用于表征驾驶员力矩问题的“四元”形式。针对此应用，引入了一种特殊的措施。