Linear Operators: General theory |
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Page 838
space of , definition , IV.2.24 ( 242 ) properties , IV.15 Annihilator of a set , II.4.17 ( 72 ) Arzelą theorem , on continuity of limit function , IV.6.11 ( 268 ) remarks concerning , ( 383 ) Ascoli - Arzelą theorem , on compactness of ...
space of , definition , IV.2.24 ( 242 ) properties , IV.15 Annihilator of a set , II.4.17 ( 72 ) Arzelą theorem , on continuity of limit function , IV.6.11 ( 268 ) remarks concerning , ( 383 ) Ascoli - Arzelą theorem , on compactness of ...
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Closed orthonormal system , definition , IV.14.1 ( 357 ) study of , IV.14 Closed set , definition , 1.4.3 ( 10 ) properties , 1.4.4–5 ( 10 ) Closed sphere , II.4.1 ( 70 ) Closed unit sphere , II.3.1 ( 59 ) Closure of a set , criterion ...
Closed orthonormal system , definition , IV.14.1 ( 357 ) study of , IV.14 Closed set , definition , 1.4.3 ( 10 ) properties , 1.4.4–5 ( 10 ) Closed sphere , II.4.1 ( 70 ) Closed unit sphere , II.3.1 ( 59 ) Closure of a set , criterion ...
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fixed point of , V.10.8 ( 457 ) Equivalence of normed linear spaces , definition , II.3.17 ( 65 ) Ergodic theorems , VII.7 , VII.8.8-10 ( 598–599 ) , VIII.4-8 . ( See also Dominated theorems , Maximal theorems , Mean theorems ...
fixed point of , V.10.8 ( 457 ) Equivalence of normed linear spaces , definition , II.3.17 ( 65 ) Ergodic theorems , VII.7 , VII.8.8-10 ( 598–599 ) , VIII.4-8 . ( See also Dominated theorems , Maximal theorems , Mean theorems ...
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Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero