The Formulation of Quantum Mechanics in Terms of Nuclear Algebras

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.