## Linear Operators: General theory |

### From inside the book

Results 1-3 of 84

Page 169

1

finite collection of disjoint sets A , , . . . , Ane such that AU . . . U An = Ec , v ( u , E )

< € , and sup \ | ( s ) - f ( t ) \ < E , j = 1 , . . . , n . 8 , tea , 2 Let A CS be a u - null ...

1

**Show**that feTM ( S , E , u ) if and only if for each ε > 0 there exists a set E , and afinite collection of disjoint sets A , , . . . , Ane such that AU . . . U An = Ec , v ( u , E )

< € , and sup \ | ( s ) - f ( t ) \ < E , j = 1 , . . . , n . 8 , tea , 2 Let A CS be a u - null ...

Page 358

a projection Sn in each of the spaces Lp , BV , CBV , AC , C ' ( k ) , 1 sps 00 , k = 0

, 1 , 2 , . . . , 00 .

**Show**that Snt is given by the formula ( SJ ) ( x ) = 12 * En ( x , y ) f ( y ) dy , and isa projection Sn in each of the spaces Lp , BV , CBV , AC , C ' ( k ) , 1 sps 00 , k = 0

, 1 , 2 , . . . , 00 .

**Show**that the range of Sn lies in C100 ) . 3**Show**that Sn + 1 ...Page 360

21

o . n . system is localized if and only if max En ( x , y ) SM ...

a finite constant K such that for f in CBV , l ( snd ) ( 2 ) SK ( v ( f , [ 0 , 27 ] ) + sup ...

21

**Show**that if | Só En ( x , x ) dz 5 M , then the convergence of Snf for a given c .o . n . system is localized if and only if max En ( x , y ) SM ...

**Show**that there existsa finite constant K such that for f in CBV , l ( snd ) ( 2 ) SK ( v ( f , [ 0 , 27 ] ) + sup ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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