## Linear Operators: General theory |

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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 .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 fixed point for a contraction in Hilbert space is also a fixed point for its ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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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 isometric isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero