Abstract
AbstractIn 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.
Publisher
Cambridge University Press (CUP)
Reference25 articles.
1. On reflexivity of a quaternion normed space;Torgasev;Novi Sad J. Math.,1997
2. On the symmetric quaternionic Banach algebras I: Geljfand theory;Torgasev;Publ. Inst. Math.,1978
3. Introduction to Tensor Products of Banach Spaces
4. [15] Ludkovsky S. V. . Unbounded operators on Banach spaces over the quaternion field. arXiv: math.OA/0404444 v1 (2004).
5. Projection operators and states in the tensor product of quaternion Hilbert modules;Horwitz;Acta Appl. Math.,1991
Cited by
17 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献