## 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 . ( Hint : Given a Cauchy sequence in X / 3 , define a subsequence for ...Page 89

In the definitions of F- and

In the definitions of F- and

**B**-**spaces**, we required the**spaces**to be complete in ... Let X be a linear**space**satisfying properties ( i ) and ( ii ) of ...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 ...### 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 | |

87 other sections not shown

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