Linear Operators: General theory |
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Page 838
... properties of , Chap . II definition , II.3.2 ( 59 ) integration , Chap . III special B - spaces , Chap . IV properties , IV.15 Baire category theorem , 1.6.9 ( 20 ) Banach limits , existence and pro- perties , II.4.22-23 ( 73 ) Banach ...
... properties of , Chap . II definition , II.3.2 ( 59 ) integration , Chap . III special B - spaces , Chap . IV properties , IV.15 Baire category theorem , 1.6.9 ( 20 ) Banach limits , existence and pro- perties , II.4.22-23 ( 73 ) Banach ...
Page 840
... properties of the closure operation , 1.4.10-11 ( 11-12 ) Cluster point , of a set , I.7.8 ( 29 ) Compact operator , in C , VI.9.45 ( 516 ) criteria for and properties of , VI.9.30-35 ( 515 ) definition , VI.5.1 ( 485 ) elementary ...
... properties of the closure operation , 1.4.10-11 ( 11-12 ) Cluster point , of a set , I.7.8 ( 29 ) Compact operator , in C , VI.9.45 ( 516 ) criteria for and properties of , VI.9.30-35 ( 515 ) definition , VI.5.1 ( 485 ) elementary ...
Page 844
... properties , V.11.1-6 ( 457-458 ) remarks on , ( 466 ) , ( 473 ) study of , V.8 Extremally disconnected , ( 398 ) F F - space , basic properties , II.1-2 definition , II.1.10 ( 51 ) examples of , IV.2.27-28 ( 243 ) Factor group ...
... properties , V.11.1-6 ( 457-458 ) remarks on , ( 466 ) , ( 473 ) study of , V.8 Extremally disconnected , ( 398 ) F F - space , basic properties , II.1-2 definition , II.1.10 ( 51 ) examples of , IV.2.27-28 ( 243 ) Factor group ...
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 ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite 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 theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ