## 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 x ¢ A , there are**disjoint**neighborhoods of A and æ . ( d ) For every pair of**disjoint**closed sets ...Page 320

... the supremum is taken over all finite collections of scalars with oil < 1 and all partitions of E into a finite number of

... the supremum is taken over all finite collections of scalars with oil < 1 and all partitions of E into a finite number of

**disjoint**sets in Σ . A number of elementary properties of the semi - variation are listed in the next 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

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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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