Abstract
In this work we analyze the convenience ofnuclear barreled b*-algebras as a better mathematicalframework for the formulation of quantum principles thanthe usual algebraic formalism in terms of C*-algebras. Unbounded operators on Hilbert spaces have anabstract counterpart in our approach. The main resultsof the C*-algebra theory remain valid. We demonstrate anextremal decomposition theorem, an adequate functional representation theorem, and anextension of the classical GNS theorem.
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Iguri, S., Castagnino, M. The Formulation of Quantum Mechanics in Terms of Nuclear Algebras. International Journal of Theoretical Physics 38, 143–164 (1999). https://doi.org/10.1023/A:1026685224464
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DOI: https://doi.org/10.1023/A:1026685224464