## Linear Operators: General theory |

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Page 15

( b ) For every pair of distinct points x and y , there are

( b ) For every pair of distinct points x and y , there are

**disjoint**neighborhoods of x and y . ( c ) For every closed set A , and every 2 & A , there are**disjoint**neighborhoods of A and x . ( d ) For every pair of**disjoint**closed sets ...Page 320

... supremum is taken over all finite collections of scalars with lail S 1 and all partitions of E into a finite number of

... supremum is taken over all finite collections of scalars with lail S 1 and all partitions of E into a finite number of

**disjoint**sets in A number of elementary properties of the semi - variation are listed in the next lemma . LEMMA .Page 461

and an arbitrary convex set is possible , provided they are

and an arbitrary convex set is possible , provided they are

**disjoint**( compare Theorem 2.8 ) . He also proved that a convex set K which is compact in the X * topology of the normed linear space X , can be separated from an arbitrary ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions 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 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