## Linear Operators: General theory |

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Page 72

1.11 ) is a

1.11 ) is a

**B**-**space**( or an F - space ) with the metric ( x + 3 ) = inf \ x + zl . zez ( Hint : Given a Cauchy sequence in X / 3 , define a subsequence for which \ XX — Xx + 1 + 31 < 2 - k , k = 1 , 2 , ... , and show that a Cauchy no ...Page 89

In the definitions of F- and

In the definitions of F- and

**B**-**spaces**, we required the spaces to be complete in their metric topology . Occasionally it is necessary to consider ... Let X be a linear space satisfying properties ( i ) and ( ii ) of Definition 1.10 .Page 398

168 ] showed that every X - convergent sequence in X * is actually X ** - convergent , and that if Y is a separable

168 ] showed that every X - convergent sequence in X * is actually X ** - convergent , and that if Y is a separable

**B**-**space**, then any operator in B ( X , Y ) is weakly compact . Goodner [ 1 ; p . 103 ] proved that the unit sphere in ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero