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 a or y is zero . Hence suppose that x0y . For an arbitrary complex number a where ...
... inequality , known as the Schwarz inequality , will be proved first . It follows from the postulates for that the Schwarz inequality is valid if either a or y is zero . Hence suppose that x0y . For an arbitrary complex number a where ...
Page 370
... 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 | x ( t ) | holds for each a in Pn . -1≤t≤ + 1 ( Hint : The function x of Exercise 75 may be ...
... 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 | x ( t ) | holds for each a in Pn . -1≤t≤ + 1 ( Hint : The function x of Exercise 75 may be ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ