## Linear Operators: General theory |

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Page 419

Then the l '

Then the l '

**topology**of X is the**topology**obtained by taking as base all sets of the form N ( p ; A , 8 ) = { 9 } \ / ( p ) -1 ( 9 ) < E , JE A } , where pe X , A is a finite subset of I'm and ε > 0 . The terms l - open and I - closed ...Page 420

in the X *

in the X *

**topology**if and only if lim , a = x weakly in the sense of Definition II.3.25 . On the other hand , if X is a subspace of yt , then each element ye y determines the linear functional f , on X defined by 1 , ( x ) = x ( y ) ...Page 512

1 , 2 , is compact in the strong operator

1 , 2 , is compact in the strong operator

**topology**. If Y is also separable , A is sequentially compact in the weak operator**topology**if and only if Ă is compact in the weak operator**topology**. 6 If Y is reflexive , then the closed unit ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero