## Linear Operators: General theory |

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Page 68

The space X is said to be weakly complete if every weak Cauchy sequence has a

weak

such a way that they become Hausdorff spaces in which the notion of

convergence ...

The space X is said to be weakly complete if every weak Cauchy sequence has a

weak

**limit**. In Chapter V , a topology is introduced in certain linear spaces insuch a way that they become Hausdorff spaces in which the notion of

convergence ...

Page 179

In view of Corollary 6.17 the class H is closed under the operation of taking

of increasing sequences . Thus to prove the theorem , it will suffice to prove that a

non - negative 2 - measurable function g is the pointwise

In view of Corollary 6.17 the class H is closed under the operation of taking

**limits**of increasing sequences . Thus to prove the theorem , it will suffice to prove that a

non - negative 2 - measurable function g is the pointwise

**limit**almost ...Page 838

17 ( 72 ) Arzelą theorem , on continuity of

concerning , ( 383 ) Ascoli - Arzelą theorem , on compactness of continuous

functions , IV . 6 . 7 ( 266 ) remarks concerning , ( 382 ) Atom , in a measure

space ...

17 ( 72 ) Arzelą theorem , on continuity of

**limit**function , IV . 6 . 11 ( 268 ) remarksconcerning , ( 383 ) Ascoli - Arzelą theorem , on compactness of continuous

functions , IV . 6 . 7 ( 266 ) remarks concerning , ( 382 ) Atom , in a measure

space ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

81 other sections not shown

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad 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 meaning measure space metric neighborhood norm operator positive measure problem Proc proof properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero