## Linear Operators: General theory |

### From inside the book

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Page

PURE AND

by : R . COURANT · L . BERS • J . J . STOKER Vol . I : Vol . I : Supersonic Flow

and Shock Waves By R . Courant and K . 0 . Friedrichs Supers Vol . II : Nonlinear

...

PURE AND

**APPLIED**MATHEMATICS A Series of Texts and Monographs Editedby : R . COURANT · L . BERS • J . J . STOKER Vol . I : Vol . I : Supersonic Flow

and Shock Waves By R . Courant and K . 0 . Friedrichs Supers Vol . II : Nonlinear

...

Page i

PURE AND

by : R . COURANT · L . BERS · J . J . STOKER Vol . I : Supersonic Flow and Shock

Waves By R . Courant and K . 0 . Friedrichs Vol . II : Nonlinear Vibrations in ...

PURE AND

**APPLIED**MATHEMATICS A Series of Texts and Monographs Editedby : R . COURANT · L . BERS · J . J . STOKER Vol . I : Supersonic Flow and Shock

Waves By R . Courant and K . 0 . Friedrichs Vol . II : Nonlinear Vibrations in ...

Page 16

ZEA By

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

continuous functions on X , with the properties : 11 ( x ) – F : ( x ) } = ( ) n + 1 Mo ,

XEA , i = 0 ...

ZEA By

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

continuous functions on X , with the properties : 11 ( x ) – F : ( x ) } = ( ) n + 1 Mo ,

XEA , i = 0 ...

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### Contents

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Three Basic Principles of Linear Analysis | 49 |

Copyright | |

50 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

analytic applied arbitrary assumed B-space Borel bounded called Chapter clear closed complex condition Consequently constant contains continuous functions continuous linear converges Corollary countably additive defined DEFINITION denote dense determined dimensional disjoint element equation equivalent everywhere Exercise exists extended field finite follows formula function defined function f given Hence Hilbert identity implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear map linear operator linear space meaning metric space neighborhood norm obtained operator positive measure space projection PROOF properties proved range reflexive regular respect satisfies scalar seen separable sequence sequentially set function Show shown statement strongly subset subspace sufficient Suppose Theorem theory tion topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero