## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 95

Page 838

space of ,

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 ,

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

( 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

fixed point of , V.10.8 ( 457 ) Equivalence of normed linear spaces ,

3.17 ( 65 ) Ergodic theorems , VII.7 , VII.8.8–10 ( 598–599 ) , VIII.4-8 . ( See also

Dominated theorems , Maximal theorems , Mean theorems , Pointwise 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 , Pointwise theorems

...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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