## 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 { Taxa e A } ...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 ...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 |

quences | 26 |

Copyright | |

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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero