## Linear Operators: General theory |

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Page 452

If A is a subset of X , and p is in A , then there exists a non - zero

by A is not dense in X . PROOF . If q¢ K , then , by 2 . 12 we can find a functional ...

If A is a subset of X , and p is in A , then there exists a non - zero

**continuous****linear**functional tangent to A at p if and only if the cone B with vertex p generatedby A is not dense in X . PROOF . If q¢ K , then , by 2 . 12 we can find a functional ...

Page 454

Let K be a compact convex subset of a locally conter

Let T : K → K be

proper closed convex subset K , CK such that T ( Kı ) CK PROOF . We may

suppose ...

Let K be a compact convex subset of a locally conter

**linear**topological space X .Let T : K → K be

**continuous**. If K contains at least two points , there exists aproper closed convex subset K , CK such that T ( Kı ) CK PROOF . We may

suppose ...

Page 513

By considering the sequence { An } defined in Exercise 11 , show that this

mapping is not

in X * ...

By considering the sequence { An } defined in Exercise 11 , show that this

mapping is not

**continuous**in the strong operator topology . 13 If U : Y * → X * is a**linear**mapping which is**continuous**with the y topology in Y * and the X topologyin X * ...

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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