## Linear Operators: General theory |

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Page 95

In some cases that will be encountered the values of u are not scalars , but customarily where integration is used in this text u is a scalar

In some cases that will be encountered the values of u are not scalars , but customarily where integration is used in this text u is a scalar

**valued**function and f a vector ( or scalar )**valued**function . Thus , even if the integration ...Page 224

It will be assumed that the reader is familiar with the elementary theory of complex

It will be assumed that the reader is familiar with the elementary theory of complex

**valued**analytic functions of one complex variable and this theory will be applied here to obtain the extensions which will be used later .Page 318

Vector

Vector

**Valued**Measures The theorems on spaces of set functions proved in the last section permit us to develop a more satisfactory theory of vector**valued**countably additive set functions ( briefly , vector**valued**measures ) than we ...### 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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### Common terms and phrases

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