## Linear Operators: General theory |

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Page 392

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

employed by Bartle [ 3 ] to obtain a Lebesgue - type integration theory where both

...

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 beenemployed by Bartle [ 3 ] to obtain a Lebesgue - type integration theory where both

...

Page 728

treatment was

generator of a group , it is possible to extend the class of functions to include

polynomials and other functions with similar growth conditions . The treatment in

...

treatment was

**given**by Phillips [ 5 ] . Bade [ 1 ] showed that for the infinitesimalgenerator of a group , it is possible to extend the class of functions to include

polynomials and other functions with similar growth conditions . The treatment in

...

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proofs , valid in uniformly convex spaces , were

Riesz [ 16 , 18 ] . Another proof , based on the interesting fact that a fixed point for

a contraction in Hilbert space is also a fixed point for its adjoint , was

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 fixed point for

a contraction in Hilbert space is also a fixed point for its adjoint , was

**given**by ...### 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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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