## Linear Operators: General theory |

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Page 138

**Consequently**, Li- , v ( u , E ; ) < 00 , and as n 0 . i = n v ( u , UE ) = Συ ( μ . Ε , ) + 0 ,**Consequently**, u ( E ) - Eu ( E ; ) Xu ( E ; ) = lu ( UE ; ) Sv ( u , u E ; ) → 0 , n - 1 i = n proving that u ( E ) . Xu ( En ) .Page 151

**Consequently**, lim sup lin - Imlo S lim sup ( SF , \ ( s ) —fm ( s ) polje , ds ) " ' ° + 2 llo { 1 . Slim sup [ { S £ . !! . ( s ) -f ( s ) p v ( u , ds ) " " + { Stem ( 8 ) — 1 ( 8 | p10 ( ja , ds ) " ' ] + 2ello m , n- > m , n - 00 1 ...Page 369

**Consequently**, unless x , ( t ) is a constant of absolute value 1 , C is a set of at most n + 1 points -1st St ... < tr S 1 , and there are constants cj , . . . , Cy with a C ; = 1 , and in terms of which we may Li \ write an ...### 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