## Linear Operators: General theory |

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Page 473

Day [ 5 ] showed that

combinations also yield uniformly convex spaces . A dual notion of “

Day [ 5 ] showed that

**uniform**convexity in the neighborhood of a point implies**uniform**convexity , and ( Day [ 4 , 6 ] ) demonstrated that under certain conditionscombinations also yield uniformly convex spaces . A dual notion of “

**uniform**...Page 841

... IV.7.6 ( 285 ) bounded functions , IV.6.18-22 ( 274–277 ) special C - spaces , (

397–398 )

IV.7.4 ( 283 ) Continuous ( or y - continuous set functions ) , criterion for , III.4.13 ...

... IV.7.6 ( 285 ) bounded functions , IV.6.18-22 ( 274–277 ) special C - spaces , (

397–398 )

**uniform**continuity , 1.6.16–18 ( 23– 24 ) of almost periodic functions ,IV.7.4 ( 283 ) Continuous ( or y - continuous set functions ) , criterion for , III.4.13 ...

Page 857

... V.10.5 ( 456 ) , ( 470 ) on product spaces , 1.8.5 ( 32 ) remarks on , ( 730 )

513 ) Unit , of a group , ( 34 ) Unit sphere in a normed space , compactness and

finite ...

... V.10.5 ( 456 ) , ( 470 ) on product spaces , 1.8.5 ( 32 ) remarks on , ( 730 )

**Uniform**operator topology , definition , VI.1.1 ( 475 ) properties , VI.9.11-12 ( 512-513 ) Unit , of a group , ( 34 ) Unit sphere in a normed space , compactness and

finite ...

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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