## 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 complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero