Linear Operators: General theory |
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Page 121
... inequality of Minkowski and ( in the case of scalar valued func- tions ) the inequality of Hölder may be regarded as applying to the spaces L. This observation is obvious in the case of Minkowski's inequality . To see that it is ...
... inequality of Minkowski and ( in the case of scalar valued func- tions ) the inequality of Hölder may be regarded as applying to the spaces L. This observation is obvious in the case of Minkowski's inequality . To see that it is ...
Page 248
... inequality , known as the Schwarz inequality , will be proved first . It follows from the postulates for that the Hence suppose that Schwarz inequality is valid if either x or y is zero . x0y . For an arbitrary complex number α 0 ≤ ( x ...
... inequality , known as the Schwarz inequality , will be proved first . It follows from the postulates for that the Hence suppose that Schwarz inequality is valid if either x or y is zero . x0y . For an arbitrary complex number α 0 ≤ ( x ...
Page 370
... inequality ' ( 0 ) ≤ n max x ( t ) | holds for each in P. If n is even , the inequality | x ′ ( 0 ) | ≤ ( n − 1 ) max | x ( t ) | holds for each x in Pn . −1≤i≤ + 1 ( Hint : The function x of Exercise 75 may be taken in the ...
... inequality ' ( 0 ) ≤ n max x ( t ) | holds for each in P. If n is even , the inequality | x ′ ( 0 ) | ≤ ( n − 1 ) max | x ( t ) | holds for each x in Pn . −1≤i≤ + 1 ( Hint : The function x of Exercise 75 may be taken in the ...
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