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 , ( 34 ) metrizable , ( 90 ) topological , II.1.1 ( 49 ) H Haar measure on a compact group , V.11.22-3 ( 460 ) Hadamard three circles theorem , VI.11.48 ( 538 ) Hahn - Banach theorem , II.3.10 ( 62 ) discussion of , ( 85-88 ) ...
... definition , ( 34 ) metrizable , ( 90 ) topological , II.1.1 ( 49 ) H Haar measure on a compact group , V.11.22-3 ( 460 ) Hadamard three circles theorem , VI.11.48 ( 538 ) Hahn - Banach theorem , II.3.10 ( 62 ) discussion of , ( 85-88 ) ...
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