## Linear Operators: General theory |

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The metric topology in X is the smallest topology containing the spheres . The set X , with its metric topology , is called a

The metric topology in X is the smallest topology containing the spheres . The set X , with its metric topology , is called a

**metric space**. If X is a topological space such that there exists a metric function whose topology is the same ...Page 20

A sequence { an } in a

A sequence { an } in a

**metric space**is a Cauchy sequence if limm , n olam , an ) = 0. If every Cauchy sequence is convergent , a**metric space**is said to be complete . The next three lemmas are immediate consequences of the definitions .Page 459

Show that K * has a continuous tangent functional at each point of a dense subset of its boundary . 14 DEFINITION . A point p of a subset A of a

Show that K * has a continuous tangent functional at each point of a dense subset of its boundary . 14 DEFINITION . A point p of a subset A of a

**metric space**is called diametral if suprea e ( p , x ) = supr , vea ( x , y ) .### What people are saying - Write a review

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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