## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 79

Page 21

A set is said to be

be nowhere

separable , if it contains a denumerable

topological ...

A set is said to be

**dense**in a topological space X , if its closure is X. It is said tobe nowhere

**dense**if its closure does not contain any open set . A space isseparable , if it contains a denumerable

**dense**set . 12 THEOREM . If atopological ...

Page 450

If a convex subset of a separable B - space X has an interior point , it has a

unique tangent at each point of a

be the convex set . It will be shown that — ( x , y ) : T ( x , -y ) , y e X , for x in a

If a convex subset of a separable B - space X has an interior point , it has a

unique tangent at each point of a

**dense**subset of its boundary . PROOF . Let Kbe the convex set . It will be shown that — ( x , y ) : T ( x , -y ) , y e X , for x in a

**dense**...Page 842

... ( 2 )

438-439 )

< p < 0C , III.3.8 ( 125 )

170 ) ...

... ( 2 )

**Dense**convex sets , V.7.27 ( 437 )**Dense**linear manifolds , 1.7.10-41 (438-439 )

**Dense**set , definition , 1.6.11 ( 21 )**density**of simple functions in L. , 1< p < 0C , III.3.8 ( 125 )

**density**of continuous functions in T11 and Lp , 111.9.17 (170 ) ...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

### Common terms and phrases

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