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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ