## Linear Operators: General theory |

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Page 154

Since it is

Since it is

**clear**that f is of bounded ... bi , with an > bn > an + 1 ) n = 1 , 2 , ... , which converge to a , such that f ( an ) -- | ( bn ) > d , and this**clearly**contradicts the fact that f is of bounded variation on ( a , b ) .Page 443

If 2 ( E ) = 2 ( EE ) and 22 ( E ) = 2 ( E ( S– E , ) ) for E € , it is

If 2 ( E ) = 2 ( EE ) and 22 ( E ) = 2 ( E ( S– E , ) ) for E € , it is

**clear**that i ,, 22 € ba ( S , L1M ) , that v ( 1 , E ) = v ( 2 , EE ) , and that v ( 7.2 , E ) v ( 2 , E ( S - E ) for * ** - 0 . > ...Page 444

For any g in L. the manifold M , = \ { fje Lo , y * ( 18 ) = y * ( 1 ) y * ( g ) } is

For any g in L. the manifold M , = \ { fje Lo , y * ( 18 ) = y * ( 1 ) y * ( g ) } is

**clearly**a closed linear manifold in Lo , and it follows from the preceding ... It is**clear**that supx * em ' * ( f ) = ||| for f € L. ( S , E , u ) .### 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