## Linear Operators: General theory |

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Page 143

Expressions such as u - simple function , totally u - measurable function , u - measurable function , u - integrable function , etc. , do not change

Expressions such as u - simple function , totally u - measurable function , u - measurable function , u - integrable function , etc. , do not change

**meaning**when u is regarded as defined on E * . This is because these expressions refer ...Page 326

Let 8x and nk have the same

Let 8x and nk have the same

**meaning**as in the previous paragraph . Since each fx is u - integrable it follows from Egoroff's theorem ( III.6.12 ) and the second paragraph of the proof of Theorem III.2.22 that there is a simple function ...Page 685

In order to be able to assign a

In order to be able to assign a

**meaning**to the averages 1 a ( ii ) A ( Q ) = ( * t T ( t ) dt , 0 SO , O. ó which are to be our basic concern in this section , it will be desirable to supplement the algebraic condition ( i ) by a ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

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