## Linear Operators: General theory |

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Page 103

For an example of such a function , let S = ( 0 , 1 ) and E be the field of finite

unions of intervals I = [ a , b ) , o Sa < b s 1 , with u ( I ) = 6 - a as in Section 1 . Let

R

F ( p ...

For an example of such a function , let S = ( 0 , 1 ) and E be the field of finite

unions of intervals I = [ a , b ) , o Sa < b s 1 , with u ( I ) = 6 - a as in Section 1 . Let

R

**denote**the set of rational points in S . For r = piqe R in lowest terms , we defineF ( p ...

Page 142

Throughout the proof the symbol E with or without subscripts will

E , the symbol M with or without subscripts will

) = 0 , and N with or without subscripts will

Throughout the proof the symbol E with or without subscripts will

**denote**a set inE , the symbol M with or without subscripts will

**denote**a set in E for which v ( u , M) = 0 , and N with or without subscripts will

**denote**a subset of a set M . To see ...Page 469

Let S ;

, Xm . Let x1

27 ) } 1 / 2 , and æ ;

Let S ;

**denote**the unit sphere in the space of variables X7 , . . . , & i - 1 , Xi + 1 , . . ., Xm . Let x1

**denote**the positive square root { 1 - ( 2 ; + . . . + x ; - ỉ + x i + ỉ + . . . +27 ) } 1 / 2 , and æ ;

**denote**the corresponding negative square root ; let po ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

21 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 Consequently constant contains converges convex Corollary defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math mean measure space metric neighborhood norm positive measure problem Proc projection PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement strongly subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero