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Representations of Semigroups
Hilbert Space Representations of Baer Semigroups
Special Baer Semigroups and Their Representations
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atom Baer property Baer ring Baer semigroup Banach algebra Boolean bounded linear operators Chapter commutative complex numbers consider convex coordinatizing Baer semigroup Corollary II.3.4 correspondence countable cp(a cp(aAb cp(e cp(l cp(q*tr cp(s cyclic vector defined definite function cp direct sum e e P'(S element Baer semigroup exists f in P'(S faithful representation finite follows Foulis Gelfand-Segal construction hermitian hermitian functional Hilbert space Hilbert space 3C Hilbert space model Hilbert space representations homomorphism implies inner product irreducible representation isomorphic left ideal Lemma linear combinations multiplication null space observable obvious one-to-one orthomodular lattice poset positive linear functional preserves Proof propositions prove q,r e quantum logic quantum mechanics s,t e satisfies property Section self-adjoint operator semicharacters semigroup of Example semiregular spectrum standard logic strong Baer representation sub-Baer semigroup subspace supp(f Suppose cp symmetric tation Theorem tion vector x0