## Linear Operators: General theory |

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Page 81

**Theorems**1.11 , 1.17 , and 1.18 were proved for linear functionals on a general B - space by Hahn [ 2 ] who applied ... Banach and Steinhaus [ 1 ; p , 53 ] observed that in the case of a Bspace**Theorem**1.11 remains valid if { Tex ] a e ...Page 82

**theorems**or to give generalizations of some**theorems**of Saks 2 , 3 ] on sequences of measures . ... Orlicz [ 7 ] proves a**theorem**of the condensation type where the double sequence of operators also depends on a parameter in a complete ...Page 729

**Theorems**for abstract vector lattices were proved by G. Birkhoff [ 2 ] , Kakutani [ 7 , 8 ] , and F. Riesz [ 17 ] . Several generalizations of the mean ergodic**theorem**to groups or semi - groups of operators more general than the ...### 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