## Linear Operators: General theory |

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**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 { Tax \ 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 ...Page 390

**Theorem**9.4 is a special case of this result and a**theorem**of Nikodým [ 6 ] , namely**Theorem**III.7.3 .**Theorem**9.8 , which strengthens the uniform boundedness**theorem**in a special case , is due to Nikodým [ 5 ] .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero