Linear Operators: General theory |
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Page 182
... defined u - almost everywhere by the formula ( αλ Edu 2 ( E ) = √ ( da ( s ) } μ ( ds ) , ΕΕΣ . We close this ... defined on S , is μ - measurable , then f ( p ( ) ) is μ1 - measurable ; ( e ) if μ2 is non - negative and countably ...
... defined u - almost everywhere by the formula ( αλ Edu 2 ( E ) = √ ( da ( s ) } μ ( ds ) , ΕΕΣ . We close this ... defined on S , is μ - measurable , then f ( p ( ) ) is μ1 - measurable ; ( e ) if μ2 is non - negative and countably ...
Page 240
... defined for a field 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 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 = La x1 f ( x ) dx , n≥ 0 , is a bounded map of L2 into l2 such that TT * is the map { a , } → { b } defined by bn = ∞ aj Σ ¿ = 0 n + j + 1 Show that T has norm √л . Show that the map S of L2 ( 0 , 1 ) into itself defined ...
... defined by an = La x1 f ( x ) dx , n≥ 0 , is a bounded map of L2 into l2 such that TT * is the map { a , } → { b } defined by bn = ∞ aj Σ ¿ = 0 n + j + 1 Show that T has norm √л . Show that the map S of L2 ( 0 , 1 ) into itself defined ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian 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