88 pages matching operator theory riesz spaces in this book
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a-order continuous algebraic arbitrary Archimedean Archimedean Riesz space assume Banach lattice Banach space Cauchy sequence Cb(E complete Riesz space continuous functions converges in norm countable decomposition Dedekind complete Dedekind cr-complete defined definition denoted directed set disjoint complement evident example Exercise exists an element F Dedekind follows Furthermore Hence holds implies increasing sequence inequality infimum Lebesgue measure Lemma linear operator linear subspace mapping natural number non-empty subset norm bounded normed Riesz space observe order bounded operator order continuous norm order dense ordered vector space partially ordered pointwise pointwise ordering positive linear functional positive operator principal projection property projection band proof prove real numbers Riesz homomorphism Riesz subspace Riesz-Fischer property satisfying Show signed measure Similarly spectral theorem sup(u supremum u-uniform Cauchy sequence u-uniformly uniformly complete upper bound upwards directed set vector space zero