## Linear Operators: General theory |

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If X and Y are topological spaces and g : X → Y , the expression lim g ( w ) = y is written to mean that for every

If X and Y are topological spaces and g : X → Y , the expression lim g ( w ) = y is written to mean that for every

**neighborhood**N , of y , there exists a**neighborhood**N. of x , such that g ( N2 ) CN ,. The following is a related ...Page 51

If V is a

If V is a

**neighborhood**of f ( y ) , then , by Lemma 2 ( c ) , Ví ( y - 1x ) is a**neighborhood**of f ( x ) . If U is a**neighborhood**of a such that f ( U ) C V / ( y - lr ) , then Ur - ly is a**neighborhood**of y such that | ( Ux - ly ) = f ...Page 56

of the image of any

of the image of any

**neighborhood**G of the element 0 in X contains a**neighborhood**of the element 0 in Y. Since a -- b is a continuous function of a and b , there is a**neighborhood**M of 0 such that M - MCG .### 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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### Common terms and phrases

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