## 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

M -

filters , 1.7.10 ( 30 ) Convergence of sequences , generalized , 1.7.1-7 ( 26–29 )

in ...

M -

**uniform**, criteria for , I11.6.2–3 ( 145 ) , III.6.12 ( 149 ) definition , III.6.1 ( 145 )**uniform**, definition , 1.7.1 ( 267 ) properties , 1.7.6–7 ( 28–29 ) Convergence offilters , 1.7.10 ( 30 ) Convergence of sequences , generalized , 1.7.1-7 ( 26–29 )

in ...

Page 857

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

topology , definition , VI.1.1 ( 475 ) properties , V1.9.11-12 ( 512–513 ) Unit , of a

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

dimensionality ...

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

**Uniform**operatortopology , definition , VI.1.1 ( 475 ) properties , V1.9.11-12 ( 512–513 ) Unit , of a

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

dimensionality ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero