## Linear Operators: General theory |

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Page 473

Day [ 5 ] showed that

Day [ 5 ] showed that

**uniform**convexity in the neighborhood of a point implies**uniform**convexity , and ( Day [ 4 , 6 ] ) demonstrated that under certain conditions combinations also yield uniformly convex spaces .Page 841

... 1.5.2 ( 15 ) extension of 1.5.3–4 ( 15–17 ) , 1.6.17 ( 23 ) representation as a C - space , almost periodic functions , IV.7.6 ( 285 ) bounded functions , IV.6.18-22 ( 274–277 ) special C - spaces , ( 397–398 )

... 1.5.2 ( 15 ) extension of 1.5.3–4 ( 15–17 ) , 1.6.17 ( 23 ) representation as a C - space , almost periodic functions , IV.7.6 ( 285 ) bounded functions , IV.6.18-22 ( 274–277 ) special C - spaces , ( 397–398 )

**uniform**continuity ...Page 857

( See Countably additive )

( See Countably additive )

**Uniform**ergodic theory , VIII.8 Variation , of a countably additive set function , III.4.7 ( 128 ) of a function , I11.5.15 ( 140 ) . ( See also Bounded variation , Total variation ) ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero