## 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**...Page 238

With the one exception of Hilbert space , each of them will consist of real or complex

With the one exception of Hilbert space , each of them will consist of real or complex

**valued**functions f , g defined on a specified domain S . Here ...Page 323

A scalar

A scalar

**valued**measurable function f is said to be integrable if there exists a sequence In } of simple functions such that ( i ) In ( s ) converges to f ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

81 other sections not shown

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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