## Linear Operators: General theory |

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Page 388

Similar results for L , 0 , 1 ) were

Similar results for L , 0 , 1 ) were

**given**( see Fréchet [ 7 ; p . 118 ] ) but they involved a preassigned orthonormal set . Other results for L2 ( 0 , 1 ) were obtained by Veress [ 2 ] . Theorem 8.17 is essentially due to Kolmogoroff ...Page 392

tion with respect to a vector valued measure which is presented here is the one

tion with respect to a vector valued measure which is presented here is the one

**given**in Bartle , Dunford and Schwartz [ 1 ] . A similar procedure has been employed by Bartle [ 3 ] to obtain a Lebesgue - type integration theory where ...Page 728

treatment was

treatment was

**given**by Phillips [ 5 ] . Bade ( 1 ) showed that for the infinitesimal generator of a group , it is possible to extend the class of functions to include polynomials and other functions with similar growth conditions .### 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 closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero