## Linear Operators: General theory |

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Results 1-3 of 85

Page 106

The

< oo , the product xet off with the characteristic

The

**functions**totally u -**measurable**on S , or , if u is understood , totally**measurable**on S are the**functions**in the closure ... If for every E in { with v ( u , E )< oo , the product xet off with the characteristic

**function**le of E is totally**measurable**, the ...Page 179

Let ( S , & , u ) be a positive measure space , f a nonnegative u -

a -

ds ) ...

Let ( S , & , u ) be a positive measure space , f a nonnegative u -

**measurable****function**defined on S and 2 ( E ) = - f ( s ) u ( ds ) , E€ E . Let g be a non - negativea -

**measurable function**defined on S . Then fg is u - measurable , and Sag ( s ) (ds ) ...

Page 180

Since every real

s ) g ( s ) u ( ds ) , EeŁ , for a real

imaginary ...

Since every real

**measurable function**is the difference of two nonnegative**measurable functions**, it follows from the theorem that [ * ] Seg ( s ) a ( ds ) = Set (s ) g ( s ) u ( ds ) , EeŁ , for a real

**measurable function**g . Since the real andimaginary ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

21 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

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