## Linear Operators: General theory |

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Page 68

If x and y are both weak

If x and y are both weak

**limits**of a generalized sequence , then for each 2 * e X * ... Its**limit**x is in the closed linear manifold determined by { xn } ...Page 126

We define the

We define the

**limit**inferior and the**limit**superior of { En } by the equations or lim inf E , un E. lim sup En nu Em 72 n = 1 men n n = 1 man If lim inf ...Page 127

It is evident that such a sequence has the

It is evident that such a sequence has the

**limit**U21 En . A non - increasing sequence { En } is one for which En ? En + 1 , n = 1 , 2 , .### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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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