## A representation theory for commutative topological algebra |

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Acad adjoint algebraic and norm Amer application arbitrary archimedian Arens assumed assumption Banach space characterization clearly closure commutative complex-valued functions containing continuous functions convex set Corollary 6.7 defined extreme ideals extreme points f is extreme f(ab f(ba fact follows Gelfand Hausdorff space hence Hilbert space Krein lattice theorem limit point linear functional linear space linear subspace M. H. Stone Math maximal ideal modulo monotone negative Neumark non-negative real non-null norm preserving fashion normed algebra order ideal order isomorphic order unit ordered algebra ordered vector space polynomial identity positive cone positive elements positive real preceding lemma proof of Theorem prove quasi-cone real algebra real Banach algebra real C(X real interval real number real-valued result self-adjoint elements self-adjoint operators set of extreme square series strictly real structure subalgebra subset supporting plane Suppose Theorem 6.3 topology two-sided inverse uniformly closed unit sphere vector lattice theorem