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 Schwarz inequality is valid if either a or y is zero . Hence suppose that x0y . For an arbitrary complex number a 0 ≤ ( x + xy , x ...
... inequality , known as the Schwarz inequality , will be proved first . It follows from the postulates for Schwarz inequality is valid if either a or y is zero . Hence suppose that x0y . For an arbitrary complex number a 0 ≤ ( x + xy , x ...
Page 370
... inequality | x ' ( 0 ) | ≤n max | x ( t ) | holds for each a in P. If n is even , the inequality | x ' ( 0 ) | ≤ ( n − 1 ) max x ( t ) | holds for each x in P. -1≤ts + 1 ( Hint : The function x of Exercise 75 may be taken in the ...
... inequality | x ' ( 0 ) | ≤n max | x ( t ) | holds for each a in P. If n is even , the inequality | x ' ( 0 ) | ≤ ( n − 1 ) max x ( t ) | holds for each x in P. -1≤ts + 1 ( Hint : The function x of Exercise 75 may be taken in the ...
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