## Linear Operators: General theory |

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Page 239

It consists of ordered n - tuples x = [ ( 1 , ... , Om ] of scalars dz . . . . , Chon and has the

It consists of ordered n - tuples x = [ ( 1 , ... , Om ] of scalars dz . . . . , Chon and has the

**norm**{ a } = { } 10 ; \ " } lin . 2 = 1 3 .Page 240

The

The

**norm**is n = sup | « il . ... 2 ) consists of all uniform limits of finite linear combinations of characteristic functions of sets in E. The**norm**in B ...Page 472

168 ] showed that the

168 ] showed that the

**norm**in C [ 0 , 1 ] is strongly differentiable at x , e C [ 0 , 1 ] if and only if the function x , achieves its maximum at exactly ...### 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