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 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 a or y is zero . Hence suppose that x0y . For an arbitrary complex number a 0 ≤ ( x ...
Page 370
... inequality | x ' ( 0 ) | ≤n max | x ( t ) | holds for each x in P. If n is even , the inequality | x ' ( 0 ) | ≤ ( n − 1 ) max | x ( t ) | holds for each x in Pn . -1≤t≤ + 1 ( Hint : The function a 。 of Exercise 75 may be taken in ...
... inequality | x ' ( 0 ) | ≤n max | x ( t ) | holds for each x in P. If n is even , the inequality | x ' ( 0 ) | ≤ ( n − 1 ) max | x ( t ) | holds for each x in Pn . -1≤t≤ + 1 ( Hint : The function a 。 of Exercise 75 may be taken in ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ