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 ...
Page 840
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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1.5.6 ( 17 ) definition , 1.5.5 ( 17 ) Finite measure ( space ) , criterion for and properties , III.4.4-9 ( 127129 ) ... ( See also Set function ) definition , III.1.2 ( 96 ) study of , III.1-3 Fixed point property , definition , V.10.1 ...
1.5.6 ( 17 ) definition , 1.5.5 ( 17 ) Finite measure ( space ) , criterion for and properties , III.4.4-9 ( 127129 ) ... ( See also Set function ) definition , III.1.2 ( 96 ) study of , III.1-3 Fixed point property , definition , V.10.1 ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero