On quaternionic functional analysis
نویسنده
چکیده
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 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. 2000 Mathematics Subject Classification: Primary 16D20, 46B04, 46C05, 46L05, 81S99; Secondary 16D90, 46B10, 46B28, 46J10
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