Linear Operators: General theory |
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Page 182
... defined u - almost everywhere by the formula 2. ( E ) = S2 Cau ( dλ Edu ( s ) } μ ( ds ) , ΕΕΣ . We close this ... defined on S is μ - measurable , then f ( p ( ) ) is μ1 - measurable ; ( e ) if μ is non - negative and countably additive ...
... defined u - almost everywhere by the formula 2. ( E ) = S2 Cau ( dλ Edu ( s ) } μ ( ds ) , ΕΕΣ . We close this ... defined on S is μ - measurable , then f ( p ( ) ) is μ1 - measurable ; ( e ) if μ is non - negative and countably additive ...
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 | μ is the total variation of μ on S , i.e. , | μ | = v ( μ , S ) . 16. The space ca ( S , E ) is defined for a o ...
... defined for a field of subsets of a set S and consists of all bounded additive scalar functions defined on 2. The norm | μ is the total variation of μ on S , i.e. , | μ | = v ( μ , S ) . 16. The space ca ( S , E ) is defined for a o ...
Page 534
... defined by an = S 1 x " f ( x ) dx , n≥ 0 , is a bounded map of L2 into l2 such that TT * is the map { a , } → { bn } defined by bn - ∞ а ; Σ ¿ = 0n + j + 1 Show that T has norm √л . Show that the map S of L2 ( 0 , 1 ) into itself ...
... defined by an = S 1 x " f ( x ) dx , n≥ 0 , is a bounded map of L2 into l2 such that TT * is the map { a , } → { bn } defined by bn - ∞ а ; Σ ¿ = 0n + j + 1 Show that T has norm √л . Show that the map S of L2 ( 0 , 1 ) into itself ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ