## Linear Operators: General theory |

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Suppose that gn ( T ) converges in the

Suppose that gn ( T ) converges in the

**uniform**operator topology to a compact operator . Let 2 € o ( T ) , and lim , ** gn ( 2 ) + 0.Page 841

u -

u -

**uniform**, criteria for , III.6.2–3 ( 145 ) , III.6.12 ( 149 ) definition , I11.6.1 ( 145 )**uniform**, definition , 1.7.1 ( 267 ) properties , 1.7.6–7 ...Page 857

... ( 470 ) on product spaces , 1.8.5 ( 32 ) remarks on , ( 730 )

... ( 470 ) on product spaces , 1.8.5 ( 32 ) remarks on , ( 730 )

**Uniform**operator topology , definition , VI.1.1 ( 475 ) properties , V1.9.11-12 ( 512-513 ) ...### What people are saying - Write a review

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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