## Linear Operators: General theory |

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Page 72

I.11 ) is a

I.11 ) is a

**B**-**space**( or an F -**space**) with the metric ( x + 3 ) = infla + 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 ...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 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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