## Linear Operators: General theory |

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( Hahn

( Hahn

**extension**) Every countably additive non - negative extended real valued set function u on a field E has a countably additive non - negative**extension**to the o - field determined by E. If u is o - finite on & then this**extension**...Page 143

Let u be a vector or extended real valued function on the o - field and let { * be defined as in the preceding theorem . Then the function u with domain 2 * is known as the Lebesgue

Let u be a vector or extended real valued function on the o - field and let { * be defined as in the preceding theorem . Then the function u with domain 2 * is known as the Lebesgue

**extension**of u . The o - field E * is known as the ...Page 554

**Extension**of Linear Transformation . Taylor [ 1 ] studied conditions under which the**extension**of linear functionals will be a uniquely defined operation . Kakutani [ 6 ] showed that this operation is linear and isometric for each ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint 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 separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero