Linear Operators: General theory |
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Page 239
... norm | x | = sup | α , ] . 1≤i≤n 4. The space l , is defined for 1 ≤ p < ∞ as the linear space of all sequences x = { x } of scalars for which the norm is finite . | x | * 00 n = 1 00 5. The space is the linear space of all bounded ...
... norm | x | = sup | α , ] . 1≤i≤n 4. The space l , is defined for 1 ≤ p < ∞ as the linear space of all sequences x = { x } of scalars for which the norm is finite . | x | * 00 n = 1 00 5. The space is the linear space of all bounded ...
Page 240
... norm is finite . n x = sup sup | Σα n i = 1 11. The space cs is the linear space of all sequences a for which the series is convergent . The norm is n 00 1 | x | 11 = sup | Σ α ; ) . n { x } of = { αn } 12 . i = 1 Let S be an arbitrary ...
... norm is finite . n x = sup sup | Σα n i = 1 11. The space cs is the linear space of all sequences a for which the series is convergent . The norm is n 00 1 | x | 11 = sup | Σ α ; ) . n { x } of = { αn } 12 . i = 1 Let S be an arbitrary ...
Page 532
... norm л ( sin л / p ) −1 , p > 1 , ( c ) ( Hardy , Littlewood , Polya ) ( T1 ) ( x ) = [ ° f ( y ) dy max ( x , y ) is a map in L , ( 0 , ∞ ) of norm p2 ( p - 1 ) -1 , p > 1 . by 22 Show that the mapping T : { a } → { b } of sequences ...
... norm л ( sin л / p ) −1 , p > 1 , ( c ) ( Hardy , Littlewood , Polya ) ( T1 ) ( x ) = [ ° f ( y ) dy max ( x , y ) is a map in L , ( 0 , ∞ ) of norm p2 ( p - 1 ) -1 , p > 1 . by 22 Show that the mapping T : { a } → { b } of sequences ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz 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