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 Schwarz inequality is valid if either x or y is zero . Hence suppose that x0y . For an arbitrary complex number a 0 ≤ ( x ...
... inequality , known as the Schwarz inequality , will be proved first . It follows from the postulates for that the Schwarz inequality is valid if either x or y is zero . Hence suppose that x0y . For an arbitrary complex number a 0 ≤ ( x ...
Page 370
... inequality holds for each x in Pn . x ' ( 1 ) ≤ n2 max x ( t ) | -1≤t≤1 80 If n is odd , the inequality | x ' ( 0 ) | ≤ n max | x ( t ) | -1st + 1 holds for each a in P. If n is even , the inequality | x ' ( 0 ) | ≤ ( n − 1 ) max ...
... inequality holds for each x in Pn . x ' ( 1 ) ≤ n2 max x ( t ) | -1≤t≤1 80 If n is odd , the inequality | x ' ( 0 ) | ≤ n max | x ( t ) | -1st + 1 holds for each a in P. If n is even , the inequality | x ' ( 0 ) | ≤ ( n − 1 ) max ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f 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 S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ