## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 72

Page 2

The set A is said to be a proper subset of the set B if A CB and A + B. The notation

ACB , or B ] A , will

A relative to a set B is the set whose elements are in B but not in A , i.e. , the set ...

The set A is said to be a proper subset of the set B if A CB and A + B. The notation

ACB , or B ] A , will

**mean**that A is a proper subset of B. The complement of a setA relative to a set B is the set whose elements are in B but not in A , i.e. , the set ...

Page 261

The space rba ( S ) is partially ordered by defining u 21 to

) for every E in the field determined by the closed sets . Similarly , the space C ( S

) is partially ordered by defining i g to

The space rba ( S ) is partially ordered by defining u 21 to

**mean**that u ( E ) 2 1 ( E) for every E in the field determined by the closed sets . Similarly , the space C ( S

) is partially ordered by defining i g to

**mean**that f ( s ) g ( s ) for all s in S.Page 357

Then , by C ( k ) we shall

BV [ 0 , 277 ] ; by Lp , 1 p < 0o , the space of functions defined and Lebesgue

measurable on the interval [ 0 , 27 ) such that Ho = { So \ | ( x ) | Pdx } 1lp < 00 ,

etc.

Then , by C ( k ) we shall

**mean**C ' ( * ) [ 0 , 27 ) ; by AC and BV , AC ( 0 , 2n ) andBV [ 0 , 277 ] ; by Lp , 1 p < 0o , the space of functions defined and Lebesgue

measurable on the interval [ 0 , 27 ) such that Ho = { So \ | ( x ) | Pdx } 1lp < 00 ,

etc.

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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