## Linear Operators: General theory |

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mutative topological group under addition , and if the mapping ( a , a ) → Ax of Ø x X ... XG into G. ( b ) In a linear

mutative topological group under addition , and if the mapping ( a , a ) → Ax of Ø x X ... XG into G. ( b ) In a linear

**topological space**X , all linear ...Page 413

non - zero linear functional on the complex space X , which separates the sets M and N. Q.E.D. 2. Linear

non - zero linear functional on the complex space X , which separates the sets M and N. Q.E.D. 2. Linear

**Topological Spaces**In this section , the results of ...Page 419

Let X be a linear vector

Let X be a linear vector

**space**, and let I be a total subspace of X * . Then the l '**topology**of X is the**topology**obtained by taking as base all sets of ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero