## Linear Operators: General theory |

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Page i

Nelson Dunford, Jacob T. Schwartz. PURE AND

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

.

Nelson Dunford, Jacob T. Schwartz. PURE AND

**APPLIED**MATHEMATICS ASeries 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

.

Page 16

XEA By

continuing inductively , one obtains a sequence Fi , i = 1 , 2 , ... , of real

continuous functions on X , with the properties : 12 \ / ( x ) – Fj ( x ) = ( 3 ) n + 1

Moe XE A and ...

XEA By

**applying**to the pair f1 , My the procedure**applied**to to , Mo , and thencontinuing inductively , one obtains a sequence Fi , i = 1 , 2 , ... , of real

continuous functions on X , with the properties : 12 \ / ( x ) – Fj ( x ) = ( 3 ) n + 1

Moe XE A and ...

Page 81

Theorems 1.11 , 1.17 , and 1.18 were proved for linear functionals on a general B

- space by Hahn [ 2 ] who

spaces . The first really general proofs of Theorems 1.11 and 1.13 were given by

...

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 specialspaces . The first really general proofs of Theorems 1.11 and 1.13 were given by

...

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Common terms and phrases

Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad 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 meaning measure space metric neighborhood norm operator positive measure problem Proc PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero