## Linear Operators: General theory |

### From inside the book

Results 1-3 of 93

Page 24

Nelson Dunford, Jacob T. Schwartz, William G. Bade. PROOF . If x e X , there is a

sequence of points an € A with an + # . Since { an } is a Cauchy sequence , and f

is

Nelson Dunford, Jacob T. Schwartz, William G. Bade. PROOF . If x e X , there is a

sequence of points an € A with an + # . Since { an } is a Cauchy sequence , and f

is

**uniformly**continuous , the sequence { f ( an ) } is also a Cauchy sequence .Page 145

A sequence of functions { { n } defined on S with values in X converges u -

{ n } converges

the ...

A sequence of functions { { n } defined on S with values in X converges u -

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

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

Page 360

which vanishes in a neighborhood of a point p the sequence ( S - 1 ) ( x )

converges to zero

En ( x , z ) dz SM , then the convergence of Snj for a given c . o . n . system is

localized if ...

which vanishes in a neighborhood of a point p the sequence ( S - 1 ) ( x )

converges to zero

**uniformly**for æ in some neighborhood of p . 21 Show that if séEn ( x , z ) dz SM , then the convergence of Snj for a given c . o . n . system is

localized if ...

### What people are saying - Write a review

User Review - Flag as inappropriate

i want to read

### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

10 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 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