Linear Operators: General theory |
Contents
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Convergence and Uniform Convergence of Generalized | 26 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension F₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space u-integrable u-measurable uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ