## Linear Operators: General theory |

### From inside the book

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Page 168

Let ( S , E , u ) be a positive measure space and G a

, M , X ) , where 1 p < 00 . Then there is a set S , in E , a sub o - field & of E ( S ) ,

and a closed

Let ( S , E , u ) be a positive measure space and G a

**separable**subset of L ( S , E, M , X ) , where 1 p < 00 . Then there is a set S , in E , a sub o - field & of E ( S ) ,

and a closed

**separable**subspace X of X such that the restriction My of u to £ ...Page 507

may be noted that the next theorem applies to every continuous linear map of L (

S , E , u ) into a

finite positive measure space , and let T be a weakly compact operator on L ( S ...

may be noted that the next theorem applies to every continuous linear map of L (

S , E , u ) into a

**separable**reflexive space . 10 THEOREM . Let ( S , E , u ) be a o -finite positive measure space , and let T be a weakly compact operator on L ( S ...

Page 854

4 ( 320 )

criterion for , V . 7 . 36 ( 438 )

. 14 ( 436 )

4 ( 320 )

**Separability**and compact sets , V . 7 . 1516 ( 437 ) of C , V . 7 . 17 ( 437 )criterion for , V . 7 . 36 ( 438 )

**Separability**and embedding , V . 7 . 12 ( 436 ) , V . 7. 14 ( 436 )

**Separability**and metrizability , V . 5 . 1 - 2 ( 426 )**Separable**sets , 1 ...### What people are saying - Write a review

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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