Linear Operators: General theory |
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Page 840
... definition , I.4.3 ( 10 ) properties , I.4.4-5 ( 10 ) Closed sphere , II.4.1 ( 70 ) Closed unit sphere , II.3.1 ( 59 ) Closure of a set , criterion to be in , 1.7.2 ( 27 ) definition , I.4.9 ( 11 ) properties of the closure operation ...
... definition , I.4.3 ( 10 ) properties , I.4.4-5 ( 10 ) Closed sphere , II.4.1 ( 70 ) Closed unit sphere , II.3.1 ( 59 ) Closure of a set , criterion to be in , 1.7.2 ( 27 ) definition , I.4.9 ( 11 ) properties of the closure operation ...
Page 844
... definition , II.3.17 ( 65 ) Ergodic theorems , VII.7 , VII.8.8-10 ( 598-599 ) , VIII.4-8 . ( See also Dominated ... definition III.1.11 ( 100–101 ) Essential singularity , definition , ( 229 ) Essential supremum , definition , III.1.11 ...
... definition , II.3.17 ( 65 ) Ergodic theorems , VII.7 , VII.8.8-10 ( 598-599 ) , VIII.4-8 . ( See also Dominated ... definition III.1.11 ( 100–101 ) Essential singularity , definition , ( 229 ) Essential supremum , definition , III.1.11 ...
Page 846
... definition and properties , 1.7.1-7 ( 26-29 ) Generator , infinitesimal of a semi- group of operators , VIII.1.6 ( 619 ) Graph , closed graph theorem , II.2.4 ( 57 ) of an operator , II.2.3 ( 57 ) Group , basic properties , I.10 definition ...
... definition and properties , 1.7.1-7 ( 26-29 ) Generator , infinitesimal of a semi- group of operators , VIII.1.6 ( 619 ) Graph , closed graph theorem , II.2.4 ( 57 ) of an operator , II.2.3 ( 57 ) Group , basic properties , I.10 definition ...
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