Linear Operators: General theory |
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Page 204
... zero and since 0 ≤ fn ( a , ) ≤ 1 it follows from the dominated convergence theorem ( 6.16 ) that there is a point so in Sa , for which fr ( s ) is defined for all n and for which the se- quence ( s ) does not converge to zero . Thus ...
... zero and since 0 ≤ fn ( a , ) ≤ 1 it follows from the dominated convergence theorem ( 6.16 ) that there is a point so in Sa , for which fr ( s ) is defined for all n and for which the se- quence ( s ) does not converge to zero . Thus ...
Page 452
... zero continuous linear functional tangent to B at p is a tangent to A at p . Conversely , if f is a non - zero continuous linear functional tangent to A at p , then Rf ( p ) = c , Rƒ ( A ) ≤ c . It follows that Rf ( a ( q — p ) + p ) ...
... zero continuous linear functional tangent to B at p is a tangent to A at p . Conversely , if f is a non - zero continuous linear functional tangent to A at p , then Rf ( p ) = c , Rƒ ( A ) ≤ c . It follows that Rf ( a ( q — p ) + p ) ...
Page 557
... zero polynomials S , i = 2 , . . . , k such that S , ( T ) x If R S1 S2S , then R ( T ) x = 0 , and consequently R ( T ) = 0 for all x e X. Thus a non - zero polynomial R exists such that R ( T ) Let R be factored as R ( 2 ) BIT1 ( 2—2 ...
... zero polynomials S , i = 2 , . . . , k such that S , ( T ) x If R S1 S2S , then R ( T ) x = 0 , and consequently R ( T ) = 0 for all x e X. Thus a non - zero polynomial R exists such that R ( T ) Let R be factored as R ( 2 ) BIT1 ( 2—2 ...
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