Notes on Spectral Theory |
Contents
Introduction | 1 |
Extensions of bounded POmeasures | 17 |
POmeasures on locally compact spaces | 39 |
Copyright | |
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A₁ assume Ax|x Baire measure Baire PO-measure Baire set Borel function Borel measure Borel sets C₁ C₂ Cartesian product commutative compact sets compact spectral measure complex spectral measure continuous complex function correspondence defined DEFINITION disjoint sets E(M₁ E₁ M₁ E₁(M₁ E₂ exists follows at once formula function f ƒ ƒ Hermitian operator Hilbert space increasingly directed integration Lemma linear form locally compact space Lx,y M₁ M₂ monotone moreover mutually disjoint normal operator notation o-ring open set pair of vectors positive operator valued projection-valued Proof Proposition quasicontinuous real polynomials real spectral measure regular weakly Borel ring S₁ S₂ semiring sequence Sf dux,y Sf dµx spectral theorem subsets Theorem 11 Theorem 23 U₂ underlying Hilbert space unique valued set function weakly Borel PO-measure weakly Borel set X₁ X₂