## Linear Operators: General theory |

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Page 182

Thus da du is

Thus da du is

**defined**u - almost everywhere by the formula lai 2 ( E ) ( s ) u ( ds ) , Εε Σ . We close this section with a generalization of many change of ...Page 240

It is evident that if we

It is evident that if we

**define**the set function u on by placing u ( E ) = 0 if ... The space B ( S ) is**defined**for an arbitrary set S and consists of all ...Page 534

function f

function f

**defined**on the interval ( 0 , 1 ) into the sequence { an }**defined**by an Sot xn f ( x ) dx , n 20 , is a bounded map of L , into l , such that TT ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

81 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