## Linear Operators, Part 1 |

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Results 1-3 of 89

Page 838

space of , definition , IV.2.24 ( 242 )

72 ) Arzelą theorem , on continuity of limit function , IV.6.11 ( 268 ) remarks

concerning , ( 383 ) Ascoli - Arzelą theorem , on compactness of continuous

functions ...

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 continuous

functions ...

Page 840

Nelson Dunford, Jacob T. Schwartz. Closed orthonormal system , definition , IV.

14.1 ( 357 ) study of , IV.14 Closed set , definition , 1.4.3 ( 10 )

( 10 ) Closed sphere , II.4.1 ( 70 ) Closed unit sphere , II.3.1 ( 59 ) Closure of a set

...

Nelson Dunford, Jacob T. Schwartz. 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

...

Page 844

... definition , III.1.11 ( 100-101 ) Essentially separably valued , definition , III.1.11 (

100-101 ) Euclidean space , definition , IV.2.1 ( 238 ) further

study of , IV.3 Extended real and complex numbers , definitions , ( 3 ) topology of

...

... definition , III.1.11 ( 100-101 ) Essentially separably valued , definition , III.1.11 (

100-101 ) Euclidean space , definition , IV.2.1 ( 238 ) further

**properties**, IV.15study of , IV.3 Extended real and complex numbers , definitions , ( 3 ) topology of

...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero