## Linear Operators: General theory |

### From inside the book

Results 1-3 of 74

Page 169

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. n . 1

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. n . 1

**Show**that fe TM ( S , E , u ) if and only if for each ε > 0 there exists a set E , € and a finite collection of disjoint sets A , ... , Ane ? such that A U .Page 358

**Show**that Snj is given by the formula ( S . } ) ( x ) = ** En ( x , y ) / ( y ) dy , and is a projection Sn in each of the spaces Lp , BV , CBV , AC , C ( K ) , 13p 300 , k = 0 , 1 , 2 , . . . , 00.**Show**that the range of Sn lies in ...Page 360

21

21

**Show**that if | S7 En ( x , x ) dz | M , then the convergence of Snf for a given c.o.n. system is localized if and only if max En ( x , y ) EM < oo for each a > 0 . 1x — v.26 22 Suppose that ( Snf ) ( x ) + f ( x ) uniformly for every ...### What people are saying - Write a review

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

### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

91 other sections not shown

### Other editions - View all

### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero