On quaternionic functional analysis
2007 ◽
Vol 143
(2)
◽
pp. 391-406
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Keyword(s):
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.
2000 ◽
Vol 36
(3-4)
◽
pp. 347-352
2017 ◽
Vol 66
(5)
◽
pp. 1054-1066
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1963 ◽
Vol 14
(2)
◽
pp. 354-354
◽
1968 ◽
Vol s1-43
(1)
◽
pp. 177-182
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1989 ◽
Vol 105
(1)
◽
pp. 139-140
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Keyword(s):
1989 ◽
Vol 105
(1)
◽
pp. 141-145