## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 87

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 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero