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 ' ( 1 ) n2 max x ( t ) holds for each x in P. 80 If n is odd , the inequality | x ′ ( 0 ) | ≤n_max | x ( t ) | -15IS + 1 holds for each a in Pn . If n is even , the inequality | x ' ( 0 ) | ≤ ( n − 1 ) max x ( t ) ...
... inequality x ' ( 1 ) n2 max x ( t ) holds for each x in P. 80 If n is odd , the inequality | x ′ ( 0 ) | ≤n_max | x ( t ) | -15IS + 1 holds for each a in Pn . If n is even , the inequality | x ' ( 0 ) | ≤ ( n − 1 ) max x ( t ) ...
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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ