## 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 , ε ) = { q ||| ( p ) -1 ( 9 ) < , 1 € A } , where pe X , A is a finite subset of I , and a > 0 . The terms I ' - open and I - closed ...Page 420

The l '

The l '

**topology**of X is often called the y**topology**of X. It is clear that a generalized sequence wr } converges to x ... this latter type of**topology**for a space of functionals occurs when y is a linear**topological**space and 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 A 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 |

Algebraic Preliminaries | 34 |

Copyright | |

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algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero