## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 93

Page 77

( 1 ) Emämn

m ; M M ( 3 ) sup In E ( amn - Om , n + u ) < 0 . M m = 0 ) The transformation

preserves sums of series ( i.e. meo ( 2n - ohmnan ) -o an ) if and only if the

equation ( 1 ...

( 1 ) Emämn

**converges**for every n ; ( 2 ) Enlamn - am , n + 1**converges**for eachm ; M M ( 3 ) sup In E ( amn - Om , n + u ) < 0 . M m = 0 ) The transformation

preserves sums of series ( i.e. meo ( 2n - ohmnan ) -o an ) if and only if the

equation ( 1 ...

Page 145

A sequence of functions { In } defined on S with values in X

uniformly if for each ε > 0 there is a set E € £ such that v ( u , E ) < ε and such that {

fn }

the ...

A sequence of functions { In } defined on S with values in X

**converges**u -uniformly if for each ε > 0 there is a set E € £ such that v ( u , E ) < ε and such that {

fn }

**converges**uniformly on S- E. The sequence { In }**converges**u - uniformly tothe ...

Page 281

Then { In }

subsequence of { { n }

implies that the condition is necessary . To prove the sufficiency , suppose that Ín

( s ) ...

Then { In }

**converges**to to at every point of S if and only if { n } and everysubsequence of { { n }

**converges**to to quasi - uniformly on A. Proof . Theorem 11implies that the condition is necessary . To prove the sufficiency , suppose that Ín

( s ) ...

### 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 | |

87 other sections not shown

### Common terms and phrases

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