## Linear Operators: General theory |

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Page 387

A detailed proof was

A detailed proof was

**given**by Fréchet [ 5 ; III . p . 441 ] . The theorem for L , [ 0 , 1 ] , 1 < p < 0 , was demonstrated by F. Riesz [ 2 ; p . 475 ] .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 ...Page 729

proofs , valid in uniformly convex spaces , were

proofs , valid in uniformly convex spaces , were

**given**by G. Birkhoff [ 7 ] and F. Riesz ( 16 , 18 ] . Another proof , based on the interesting fact that a ...### 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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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