## Linear Operators: General theory |

### From inside the book

Results 1-3 of 83

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

... every bounding point , the next theorem gives a strong result in this direction . 8

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

has a unique tangent at each point of a

... every bounding point , the next theorem gives a strong result in this direction . 8

THEOREM . 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 .Page 842

7 ( 128 ) , III . 4 . 11 ( 130 ) Lebesgue decomposition , III . 4 . 14 ( 132 ) Saks

decomposition , IV . 9 . 7 ( 308 ) Yosida - Hewitt decomposition , ( 233 ) De

Morgan , rules of , ( 2 )

manifolds , V . 7 .

7 ( 128 ) , III . 4 . 11 ( 130 ) Lebesgue decomposition , III . 4 . 14 ( 132 ) Saks

decomposition , IV . 9 . 7 ( 308 ) Yosida - Hewitt decomposition , ( 233 ) De

Morgan , rules of , ( 2 )

**Dense**convex sets , V . 7 . 27 ( 437 )**Dense**linearmanifolds , V . 7 .

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad domain elements 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 operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen semi-group 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