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On quaternionic functional analysis

Published online by Cambridge University Press:  01 September 2007

CHI-KEUNG NG
CHI-KEUNG NG*
Affiliation:
The Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, P.R. China. email: ckng@nankai.edu.cn
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Abstract

In this paper, 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 the main results in [12] (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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 2 , September 2007 , pp. 391 - 406
Copyright
Copyright © Cambridge Philosophical Society 2007

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