关于四元数泛函分析
On quaternionic functional analysis
摘要：
本文证明了四元数向量空间范畴、四元数希尔伯特空间范畴（单侧和双侧）和四元数$B^*$ -代数范畴分别等价于实向量空间范畴、实希尔伯特空间范畴和实$C^*$ -代数范畴。我们还将给出四元数希尔伯特空间的Riesz表示定理，并将推广Kulkarni的两个结果（即，我们将给出四元数$B^*$ -代数的Gelfand-Naimark定理和Gelfand定理的完整版本）.在得到这些结果的过程中，我们比较、澄清和统一了文献中的“四元数希尔伯特空间“一词。
英文摘要：
In this article, we will show that the category of quaternion vector spaces, the category of (both one-sided and two sided) quaternion Hilbert spaces and the category of quaternion $B^*$-algebras are equivalent to the category of real vector spaces, the category of real Hilbert spaces and the category of real $C^*$-algebras respectively. We will also give a Riesz representation theorem for quaternion Hilbert spaces and will extend two results of Kulkarni (namely, we will give the full versions of the Gelfand-Naimark theorem and the Gelfand theorem for quaternion $B^*$-algebras). On our way to these results, we compare, clarify and unify the term "quaternion Hilbert spaces" in the literatures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
