## Linear Operators: General theory |

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PURE AND

PURE AND

**APPLIED**MATHEMATICS A Series of Texts and Monographs Edited by : R. COURANT . L. BERS J. J. STOKER Vol . I : Supersonic Flow and Shock Waves By R. Courant and K. 0. Friedrichs Vol . II : Nonlinear Vibrations in Mechanical and ...Page 16

XEA By

XEA By

**applying**to the pair f1 , My the procedure**applied**to fo : Mo , and then continuing inductively , one obtains a sequence Fi , i = 1 , 2 , ... , of real continuous functions on X , with the properties : n \ / ( x ) – Ë F ...Page 81

Theorems 1.11 , 1.17 , and 1.18 were proved for linear functionals on a general B - space by Hahn [ 2 ] who

Theorems 1.11 , 1.17 , and 1.18 were proved for linear functionals on a general B - space by Hahn [ 2 ] who

**applied**these results to a large number of special spaces . The first really general proofs of Theorems 1.11 and 1.13 were given ...### 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 | |

91 other sections not shown

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### Common terms and phrases

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