B*-algebra representations in a quaternionic Hilbert module

A. Soffer; L. P. Horwitz

doi:10.1063/1.525656

B*-algebra representations in a quaternionic Hilbert module

A. Soffer, L. P. Horwitz

Research output: Contribution to journal › Article › peer-review

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Abstract

It is shown that the Gel'fand-Naimark-Segal (GNS) construction can be generalized to real B*-algebras containing an algebra *-isomorphic to the quaternion algebra by the use of quaternion linear functionals and Hilbert Q-modules. An extension of the Hahn-Banach theorem to such functionals is proved.

Original language	English
Pages (from-to)	2780-2782
Number of pages	3
Journal	Journal of Mathematical Physics
Volume	24
Issue number	12
DOIs	https://doi.org/10.1063/1.525656
State	Published - 1982
Externally published	Yes

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abstract = "It is shown that the Gel'fand-Naimark-Segal (GNS) construction can be generalized to real B*-algebras containing an algebra *-isomorphic to the quaternion algebra by the use of quaternion linear functionals and Hilbert Q-modules. An extension of the Hahn-Banach theorem to such functionals is proved.",

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B*-algebra representations in a quaternionic Hilbert module

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