## Linear Operators, Part 1 |

### From inside the book

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Page i

Nelson Dunford, Jacob T. Schwartz. PURE AND

Series of Texts and Monographs Edited by : R . COURANT · L . BERS - J . J .

STOKER Vol . I : Vol . II : Vol . III : Supersonic Flow and Shock Waves By R .

Courant ...

Nelson Dunford, Jacob T. Schwartz. PURE AND

**APPLIED**MATHEMATICS ASeries of Texts and Monographs Edited by : R . COURANT · L . BERS - J . J .

STOKER Vol . I : Vol . II : Vol . III : Supersonic Flow and Shock Waves By R .

Courant ...

Page 16

XEA By

continuing inductively , one obtains a sequence Fi , i = 1 , 2 , . . . , of real

continuous functions on X , with the properties : \ f ( x ) – 3 F ( r ) ] 5 ( 3 ) n + 140 ,

we A , and ...

XEA By

**applying**to the pair f1 , My the procedure**applied**to to , Mo , and thencontinuing inductively , one obtains a sequence Fi , i = 1 , 2 , . . . , of real

continuous functions on X , with the properties : \ f ( x ) – 3 F ( r ) ] 5 ( 3 ) n + 140 ,

we A , and ...

Page 81

18 were proved for linear functionals on a general B - space by Hahn [ 2 ] who

proofs of Theorems 1 . 11 and 1 . 13 were given by Hildebrandt [ 2 ] in the case of

...

18 were proved for linear functionals on a general B - space by Hahn [ 2 ] who

**applied**these results to a large number of special spaces . The first really generalproofs of Theorems 1 . 11 and 1 . 13 were given by Hildebrandt [ 2 ] in the case of

...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

12 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

Akad 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 isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric 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