## Linear Operators: General theory |

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The best known example of Theorem 2 and its

The best known example of Theorem 2 and its

**Corollary**6 is obtained by taking ( Si , Ei , Mi ) to be the Borel - Lebesgue measure on the real line for i = 1 ...Page 246

The following

The following

**corollary**was established during the first part of the preceding proof . 7**COROLLARY**. If { bz , ... , bn } is a Hamel basis for the normed ...Page 422

11

11

**COROLLARY**. Let f be a linear functional on the linear space X , and let be a total subspace of X * . Then the following statements are equivalent : ( i ) ...### 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 | |

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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