Linear Operators: General theory |
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Page 177
Nelson Dunford, Jacob T. Schwartz. may be assumed that & is real valued . A real valued set function can be represented as the ... assumed to be positive and measurable we can put F { ss e F , f ( s ) ≤ n } . Then F = UF , and v ( 2 , F ) ...
Nelson Dunford, Jacob T. Schwartz. may be assumed that & is real valued . A real valued set function can be represented as the ... assumed to be positive and measurable we can put F { ss e F , f ( s ) ≤ n } . Then F = UF , and v ( 2 , F ) ...
Page 278
... assumed that x * } = x * f . Then there is a point s in S such that x * f = f ( s ) , f € C ( S ) . PROOF . By the preceding lemma a * is a point in the space S1 de- fined in the proof of Theorem 18. By Theorem 22 , S is homeomorphic to ...
... assumed that x * } = x * f . Then there is a point s in S such that x * f = f ( s ) , f € C ( S ) . PROOF . By the preceding lemma a * is a point in the space S1 de- fined in the proof of Theorem 18. By Theorem 22 , S is homeomorphic to ...
Page 650
... assumed that │P „ ( 2 ) ƒ ( 2 ) | ≤ M in a strip | R ( 2 ) | < w + ɛ , where ε is independent of n . In the first paragraph of the proof of Lemma 7 it was seen that | R ( 2 , A ) | is uniformly bounded in any half plane R ( ) > + ε ...
... assumed that │P „ ( 2 ) ƒ ( 2 ) | ≤ M in a strip | R ( 2 ) | < w + ɛ , where ε is independent of n . In the first paragraph of the proof of Lemma 7 it was seen that | R ( 2 , A ) | is uniformly bounded in any half plane R ( ) > + ε ...
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