Linear Operators: General theory |
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Page 18
... compact space to a Hausdorff space is a homeomorphism . PROOF . Let X be a compact space , Y a Hausdorff space , and ƒ a one - to - one continuous function on X , with f ( X ) = Y. According to the preceding lemma , a closed set A in X is ...
... compact space to a Hausdorff space is a homeomorphism . PROOF . Let X be a compact space , Y a Hausdorff space , and ƒ a one - to - one continuous function on X , with f ( X ) = Y. According to the preceding lemma , a closed set A in X is ...
Page 276
... compact Hausdorff space S1 and a one - to - one embedding of S as a dense subset of S1 such that each f in X has a unique continuous extension f1 to S1 , and such that the correspondence f f is an isometric iso- morphism of A and C ( S1 ) ...
... compact Hausdorff space S1 and a one - to - one embedding of S as a dense subset of S1 such that each f in X has a unique continuous extension f1 to S1 , and such that the correspondence f f is an isometric iso- morphism of A and C ( S1 ) ...
Page 516
... compact Hausdorff space and a continuous function on S to S. Show that there is a regular countably additive non - negative measure μ defined for all Borel sets in S with the prop- erties that μ is not identically zero and u is p ...
... compact Hausdorff space and a continuous function on S to S. Show that there is a regular countably additive non - negative measure μ defined for all Borel sets in S with the prop- erties that μ is not identically zero and u is p ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ