## 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 both ...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 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