## Linear Operators: General theory |

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Page 195

with

with

**respect**to one variable and then with**respect**to the other , or vice versa . Indeed , according to Tonelli's theorem , both these integrals are equal ...Page 306

The functions un are all continuous with

The functions un are all continuous with

**respect**to the measure defined by 1 v ( un , E ) 2 ( E ) = ? Εε Σ . n = 1 2 " 1 + u ( un , E ) and thus all belong ...Page 341

( ii ) There is a non - negative u in ba ( S , E ) with

( ii ) There is a non - negative u in ba ( S , E ) with

**respect**to which every â in K is continuous . ( iii ) lim , Uq2 = 2 uniformly with**respect**to l € K.### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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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