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
Preliminary Concepts | 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 ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f 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 S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ