B*-algebra representations in a quaternionic Hilbert module

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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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