On quaternionic functional analysis

• Autores: Chi-Keung Ng
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 143, Nº 2, 2007, págs. 391-406
• Idioma: inglés
• DOI: 10.1017/s0305004107000187
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• Resumen

  • 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.