Linear Operators: General theory |
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Page 182
... defined u - almost everywhere by the formula 2 ( E ) = E ( dλ \ dμ · S ( 4 ) μ ( ds ) , ΕΕΣ . We close this section ... defined on S , is μ2 - measurable , then f ( $ ( · ) ) is M1- 1 - measurable ; ( e ) if u is non - negative and ...
... defined u - almost everywhere by the formula 2 ( E ) = E ( dλ \ dμ · S ( 4 ) μ ( ds ) , ΕΕΣ . We close this section ... defined on S , is μ2 - measurable , then f ( $ ( · ) ) is M1- 1 - measurable ; ( e ) if u is non - negative and ...
Page 240
... defined for a field Σ of subsets of a set S and consists of all bounded additive scalar functions defined on 2. The norm u is the total variation of μ on S , i.e. , │μ | = v ( μ , S ) . 16 . The space ca ( S , E ) is defined for a σ ...
... defined for a field Σ of subsets of a set S and consists of all bounded additive scalar functions defined on 2. The norm u is the total variation of μ on S , i.e. , │μ | = v ( μ , S ) . 16 . The space ca ( S , E ) is defined for a σ ...
Page 534
... defined by an - = S Son xn f ( x ) dx , n 0 , is a bounded map of L2 into l2 such that TT * is the map { a } → { bn } defined by bn = 00 aj Σ j = 0n + j + 1 Show that T has norm √л . Show that the map S of L2 ( 0 , 1 ) into itself defined ...
... defined by an - = S Son xn f ( x ) dx , n 0 , is a bounded map of L2 into l2 such that TT * is the map { a } → { bn } defined by bn = 00 aj Σ j = 0n + j + 1 Show that T has norm √л . Show that the map S of L2 ( 0 , 1 ) into itself defined ...
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