## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 76

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

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 )

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 , 1 . 6 . 16 - 18 ( 2324 ) of almost periodic functions , IV .Page 857

5 ( 32 ) remarks on , ( 730 )

properties , VI . 9 . 11 - 12 ( 512 - 513 ) Unit , of a group , ( 34 ) Unit sphere in a

normed space , compactness and finite dimensionality of , IV . 3 . 5 ( 245 ) ...

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 dimensionality of , IV . 3 . 5 ( 245 ) ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

25 other sections not shown

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### Common terms and phrases

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