## Linear Operators: General theory |

### From inside the book

Results 1-3 of 79

Page 171

every Borel set . 24

property that for every covering of S by a finite number of open sets G , . . . , Gn

there ...

**Suppose**that every continuous function is u - measurable . Show that I * containsevery Borel set . 24

**Suppose**that S is a compact topological space , with theproperty that for every covering of S by a finite number of open sets G , . . . , Gn

there ...

Page 225

Let U be a bounded open set in the complex plane , and let B denote the

boundary of U . We

rectifiable Jordan curves ; that is , we

union ...

Let U be a bounded open set in the complex plane , and let B denote the

boundary of U . We

**suppose**that B consists of a finite collection of disjoint closedrectifiable Jordan curves ; that is , we

**suppose**that B can be decomposed into theunion ...

Page 360

Show that there exists a finite constant K such that for f in CBV , | ( S . f ) ( x ) S K (

v ( f , [ 0 , 29 ] ) + sup \ | ( x ) ] ) , O S x 5 27 . OSX3217 23

x ) ( x ) uniformly in x for f in AC . ( ii ) The convergence of Sn is localized .

Show that there exists a finite constant K such that for f in CBV , | ( S . f ) ( x ) S K (

v ( f , [ 0 , 29 ] ) + sup \ | ( x ) ] ) , O S x 5 27 . OSX3217 23

**Suppose**that ( i ) ( Snf ) (x ) ( x ) uniformly in x for f in AC . ( ii ) The convergence of Sn is localized .

### What people are saying - Write a review

User Review - Flag as inappropriate

i want to read

### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

5 other sections not shown

### Other editions - View all

### Common terms and phrases

Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad domain elements equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero