## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 86

Page 136

( Hahn

valued set function u on a field E has a countably additive non - negative

is unique .

( Hahn

**extension**) Every countably additive non - neg . ative extended realvalued set function u on a field E has a countably additive non - negative

**extension**to the o - field determined by E . If u is o - finite on Ethen this**extension**is unique .

Page 143

Then the function u with domain 2 * is known as the Lebesgue

The o - field { * is known as the Lebesgue

E , and the measure space ( S , * , u ) is the Lebesgue

Then the function u with domain 2 * is known as the Lebesgue

**extension**of u .The o - field { * is known as the Lebesgue

**extension**( relative to u ) of the o - fieldE , and the measure space ( S , * , u ) is the Lebesgue

**extension**of the measure ...Page 554

the

[ 6 ] showed that this operation is linear and isometric for each closed linear ...

**Extension**of Linear Transformation . Taylor [ 1 ] studied conditions under whichthe

**extension**of linear functionals will be a uniquely defined operation . Kakutani[ 6 ] showed that this operation is linear and isometric for each closed linear ...

### 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 | |

12 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

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element 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 meaning measure space metric neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero