## 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

LEA By

LEA By

**applying**to the pair ( 1 Mo 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 : \ f ( a ) - 2 F ( x ) | S ...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 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

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